You might not know this, because I've never played a high profile tournament with it, but I actually like Living End quite a bit. I've almost played it many times—during PT Oath of the Gatewatch, I was undecided between Living End and Eldrazi until 2 days before the tournament (though in the end I decided on Eldrazi because I'm very smart).
Living End deck lists have stayed relatively constant since the deck's inception because you were always very limited in what you could play—you needed a high concentration of cyclers and you couldn't play anything that costs 2 or less, and they never printed new cyclers or good 3+ mana spells for the deck, so there hasn't been anything to change. Amonkhet finally brings a chance to update the deck, in two ways.
The first is with new cyclers, as there are a variety of new cycling creatures in all colors that are much better than what we had before. The second is the rules change regarding split cards—it used to be that cascade would hit the spell if either part cost 2 or less, but now the whole card has to cost 2, which allows you to play cheaper interaction that wasn't available before.
You might be inclined to dismiss the first part—it's just more cyclers, whatever—but it's actually huge. Living End has one major strength that almost no deck shares—it's remarkably consistent. You're going to do the same thing every. Single. Game.
As a counterpoint, Living End also has one major flaw—what it does every single game is not that good. You're more consistent than anyone, but you're consistently mediocre.
New cyclers make what you're doing better. You're still going to do the same thing every game, but now that thing is going to be faster and more powerful, and that's huge.
In practice, what Amonkhet does for the deck is speed up its goldfish by a significant amount, often a turn or even more. Cycling a Desert Cerodon adds twice as much power to the board than cycling a Deadshot Minotaur, for the exact same cost. The influx of high-power, 1-mana cyclers means you can actually compete on the speed axis, which was a fight you almost always lost before. Cards like Desert Cerodon and Horror of the Broken Lands seem innocuous, but they are to Living End what Monastery Swiftspear is to Burn decks—a way to speed your clock considerably, by themselves.
There are two ways you can build Living End now: Straight Jund, like before, or with blue. I believe straight Jund is better, so I will focus on that, but I'll address the blue builds after that in case you're a more adventurous person than I am.
The New: Cyclers
Let's take a look at the new cards we get from Amonkhet:
Archfiend of Ifnir
This is the most powerful cycling creature ever printed (unless there's some creature with a huge cycling cost that I'm not remembering). It's certainly the best one you can currently play in Living End. It has a better body than anything else, and the effect will win you the game—it's not uncommon to still have cyclers in hand when you cast Living End, and this will make sure your opponent can't just block and survive or brick wall you with a big Tarmogoyf.
The biggest issue with Archfiend is that it doesn't compete with any single creature, but with 2 creatures. Sure, cycling it is better than cycling Desert Cerodon or Monstrous Carabid, but is it better than cycling Desert Cerodon and Monstrous Carabid? Because that's what you're replacing it with.
The version of Living End that I think should be played is one with a focus on goldfishing, and right now you have enough 1-mana cyclers to make sure you're using your mana all the time. Cycling two cards instead of Archfiend not only digs you one card deeper (which can lead to finding a cascade spell or just more cyclers), but it puts two bodies into the graveyard instead of one.
My inclination is that it's not good enough to play—I'd rather just have all 1-mana cyclers. But if you play any 2-mana cycler, it should always be Archfiend (sorry Jungle Weaver, but you've been a Modern playable card for far too long).
Horror of the Broken Lands
I was already thrilled when I drew Monstrous Carabid, and this card is significantly better. Not only does it not have to suicide itself into Tarmogoyf from time to time, but it also enables a faster goldfish with its second ability. If you have just 2 Horror of the Broken Lands in play and you cycle 3 cards, they're dead! Just wait for the tilt as you're empty handed and chain triple-cyclers to kill them.
If Horror of the Broken Lands is Monastery Swiftspear, this is Goblin Guide. 6 power for only 1 mana is so much, and having this guy in your opening hand is going to do wonders for your clock. On top of it all, you can use Simian Spirit Guide to cycle it.
The Old: Split Cards
You also gain a few cards from the new split-card rule:
Dead // Gone
Dead // Gone offers the cheapest interaction you can find in a Living End deck—just 1 mana. It is great at buying you time to find or cast Living End, and it can deal with troublesome creatures such as Thalia, Ethersworn Canonist, or any Meddling Mage variant. On top of that, you can kill a sacrifice outlet (such as Viscera Seer) before the opponent can sacrifice their board in response to your Living End.
Dead // Gone does have one small issue, and it's that the creatures that you kill are always going to come back after you Living End. In this regard, it competes with Shriekmaw, which costs 1 more mana and is sorcery speed but actually adds a body for you instead of a body for them post-Living End.
My inclination is that Dead // Gone is not a good main-deck card because you just don't need this kind of effect. Living End already kills all creatures, and the deck is now fast enough that you can just Living End earlier than before and still have good board presence.
It could, however, be a good sideboard card in matchups where Shriekmaw is a bit slow. Take Burn—the accepted card to sideboard against Burn is Brindle Boar. But now, you can add so much power to the board so quickly that you could just race them, and that's much easier to do if you can kill their early creatures. You don't care that they come back later, as your board is going to be so much better by then that their 2/2 will be irrelevant. I don't think Dead // Gone replaces Brindle Boar completely, but I think a combination is likely correct.
Wear // Tear
Ingot Chewer is a much better Wear in the Living End deck, so it's a question of whether you want Tear. The two strongest pieces of hate in the format are enchantments—Leyline of the Void and Rest in Peace—so having a way to answer them for only 1 mana is appealing, but at the same time you have to add white to your deck, and I'm not a huge fan of that. I think that Beast Within can already deal with most of the problematic enchantments, and you don't need to add another color just for this effect. If you have a rainbow mana base, however, then you probably do want Wear // Tear in some numbers.
Bound // Determined
I've seen some people playing this in lists with blue, but I think Ricochet Trap is just a better card.
Crime // Punishment
I've also seen people playing Crime // Punishment, but I don't understand what for exactly. The card could be good against a deck like Affinity, but I have a hard time imagining a scenario where I actually want to tap out for it instead of just casting a Living End.
The Deck List
With the addition of the new cyclers, Living End should adopt a faster approach—you're going to be racing your opponent while killing all their creatures. This means you should opt for turn-3 Living Ends, or, at worst, turn 4. Between Simian Spirit Guide, the new high-powered cyclers, Street Wraith, and potentially Faerie Macabre, it's not unrealistic to present 20 power on turn 3, and this is on par with the other combo decks in the format.
I didn't like Faerie Macabre in the main deck before, and now I do. First, Living End has gotten more popular because of the new cyclers, so it's good to have an edge in the mirror (or against Dredge). Second, it's great against any sort of sacrifice outlet such as Viscera Seer or Arcbound Ravager. Third, I think you now actually want the free 2/2 body. Before, you were either using Living End to kill them over two turns or you were flooding the board so much that they were going to be dead in a turn no matter what, but now the 2 damage can actually make a difference. It also pumps Horror of the Broken Lands.
Another card that I think has improved is Architects of Will. Sure, it's a smaller body than what we're used to, but the ability is more relevant because games are faster, and now you want to have more black mana to accommodate Horror of the Broken Lands. Given that I want to play a ton of main-deck Faerie Macabre, I think it's better than Deadshot Minotaur (and you can reduce your dependence on green mana, which is now just for Violent Outburst).
The card that I think got worse is Fulminator Mage. I like it in Living End, but I think it's more of a sideboard card now. The opportunity cost is higher, as you have better uses for your mana. I just want to cycle, cycle, and then cast a massive Living End. I do like being able to go turn-2 Fulminator Mage with Simian Spirit Guide, but I don't think you need it anymore in racing matchups. My main deck has 2, and I think you should often sideboard them out on the draw. It's also possible that it should be 2 Beast Withins and 1 Fulminator Mage, but I think 3 is about as many as you want for this kind of effect.
This is how I would build the deck right now:
There's a chance that Demonic Dread becomes worse in this version since you have fewer Beast Within tokens and fewer Fulminators to target, but I think it's rarely going to be a problem, and worst-case scenario you can try hardcasting a Faerie Macabre. It's possible you should play Dryad Arbor, but then you need more green fetches. I don't want to play a Forest when the only green card I really want to cast is Violent Outburst.
Now, what if you were to add blue? This is what you gain:
Curator of Mysteries
This is the big payoff for branching into a 4th color. As a body, Curator of Mysteries is amazing for only 1 mana, and it's also easily the best of your creatures to hard cast. On the other hand, a big part of why this deck is good (and consistent) is its mana base, and cycling for blue is tough to achieve.
In Modern, there are 3 cascade cards you can play: Ardent Plea, Demonic Dread, and Violent Outburst. The only 3-color combination that lets you play 2 of them is Jund. You can cut green (you don't need it for any cyclers), but Violent Outburst is far and away the best cascader (not only is it an instant, but it also helps your goldfish post-Living End), and if you cut green you have to add both blue and white.
If you want to play Curator of Mysteries, I think you have to simply add blue to the existing mana base. Your mana base is going to be more painful, and might have to include rainbow lands, as having several R/G duals that can't cycle Curator or Horror of the Broken Lands, or U/G lands that can't cycle Cerodon or Horror, doesn't seem optimal.
As Foretold has been making waves online as a card that can cast the suspend spells for free. I'm a big fan of casting Ancestral Vision for free, and Restore Balance can be good too (especially since it stays in play after the Restore Balance, allowing you to win the game even if you go down to 0 mana sources), but I don't think it's good for Living End. Cascading into something requires just the cascade spell, of which you have 8, but As Foretold'ing into it requires both the As Foretold and the Living End itself, which makes it a 2-card combo.
This enables certain decks to play 1- and 2-mana cards, but that's not what Living End wants to do anyway. You need your namesake, you need to have those cascade spells, and you need the cyclers, so you're already constrained in deckbuilding. At this point I'd rather just keep the cascade spells and not add another color. If I really wanted this kind of effect, I'd play Kari Zev's Expertise.
Drake Haven doesn't belong in the main deck, but I think it can be a good sideboard card against decks that will attack your graveyard, as it can win the game single-handedly. The main question is whether it's better to have Drake Haven and go around their hate or to just face their hate head-on (by killing the hate piece). I think if all you care about is the hate then it's better to try to deal with it (with Wear // Tear or Beast Within), but, since Drake Haven also looks like a pretty good card versus control, I think it's worth trying out, as it mitigates the need for Ricochet Trap.
Blue Living End
This is a much more painful mana base, but I see no way to support blue, black, and red 1-mana cyclers on top of Violent Outburst that doesn't involve City of Brass and more fetchlands, so I think it's what you have to do. Ultimately you're still a bit short on green sources for Outburst, and I don't think the costs outweigh the gains (which are basically a better cycler and a sideboard card), but if someone who is more math-savvy than I am can come up with a great mana base then I think it would work out.
As for playing the deck, it's straightforward—just cycle and eventually cast a cascade spell to find Living End, which will hopefully win the game. If you're new to Magic or to Modern, I strongly recommend this deck, as the learning curve is significantly lower than most decks, while remaining very competitive.