There are a few things, really. Obviously, this is my personal list and things may be better or worse for other people, but:
* Bounded accuracy means that the world doesn't have to scale to the players. I spend more time thinking about how I want the world to look and less time translating my original ideas to match the party's current level.
* Advantage/Disadvantage is a great mechanic to reward or penalise the party for their actions. 4e had combat advantage for pure combat, but Advantage can be applied in any situation as a generic "You came up with a good idea that should net you a reward" mechanic.
* Because of bounded accuracy, I don't need to look for more powerful creatures as often. I've used the 4e conversion suggestions that were posted here a while back to convert some creatures that are iconic to one of my campaigns ("Agents of the Eye"). I can keep using those creatures, knowing that I can vary their numbers or allies to get the right encounter. Not that I'm going to make every relevant encounter have one of them, but it means I can add one to an existing encounter down the line and the party will know (or think

) that a particular in-campaign group is involved... and they'll still be useful, even if the party has gained levels.
* Encounter building is no worse than 4th edition, to me - and therefore it is easier (again, to me) than 3e or 2e.
* The exploration rules are nice. If we weren't moving to 5e, I'd be porting them to 4e right now. They're likely going to be yoinked for our 3e games.
* From a design point of view, I find character creation to be more flexible than 4th edition*. As a GM running a lot of 5e one-offs, it's been really good that I can say things like "All of your characters start as members of a thieves guild. Generate any character that has at least one choice that speaks to that." or "Generate any character that's trained in Arcana" in order to start out a short game with a particular style without restricting the players much. (The former was even better when the cleric had the Trickster deity option, although the Paladin of Vengeance they added can work perfectly as a Guild enforcer. I expect the full game will have the Trickster deity again. If not, it'll be easy to houserule).
There's quite a few other things, too, but they're smaller and not all from a pure DM perspective (for instance, the Thaumaturgy and Druidcraft cantrips make me incredibly happy. They're just the sort of thing that my players will use for great roleplay effect, and they're the sort of thing that *should* exist in the D&D world. In fact, my most generic reason for liking D&D Next as a system is exemplified by things like this: In lots of places, the system has loosened up old restrictions or added new capabilities that support the narrative of *being* a character of that race, class or whatever better. Two random things: The way the Fighter and Barbarian classes are both good at combat in different ways (Fighters do more damage on average, while Barbarians *appear* to because they're swingier. Training and skill against ferocity). Or the way that a magic user can choose to leave a slot or two unprepared, then wander off to study a spellbook (or pray) to solve a new problem. It'll take long enough that it's not a workable solution inside combat, but the idea of the cleric praying for a solution to a problem or a Wizard consulting their notes *works*, to me)
... I'm going to stop before my parenthesis-nesting gets worse. Needless to say, there's a ton of stuff I like. It's very much not a case of 4th edition being bad - just that I feel 5e fits my mindset and expectations of how things should work better.
* What I mean by more flexible is that, given the quantity of material in the playtest, I think it's able to create a wider variety of functional concepts at 1st level than 4e would be able to in the same number of pages. Fourth edition has vast amounts more content, of course, and a lot of it is really high quality. But 5e gets more potential variety from fewer distinct elements, I think, because it reuses them cleverly.