What 4e did well:
- The Warlord rocked. This was by far the coolest class introduced by 4e. If you never played, he was somewhat like a fighter, but his powers were focused mainly on granting extra attacks and bonuses to other players. The Warlord was a fan favorite and returns in 5e...sort of. With the right character options and feats, a 5e Fighter can be a reasonable facsimile of a 4e Warlord.
- Balance. As much as 3.5 fans insisted a godlike Wizard and a useless Fighter at high levels is somehow "core" to the D&D experience (this is in fact an artifact of 3.x), a game with "trap" classes is a broken game. Not every class in 4e was equally well designed, but you didn't have this problem of "Okay, Sam's wizard is basically godlike now and can do everything my rogue can do...so either you let me roll a new character, or I quit." Every class played its part, and every class was equally engaging to play.
- Combat was deep and engaging. There's really nothing quite like a well-executed 4e battle. Each class's and monster's unique powers and abilities interacted to create interesting battle situations that I've not seen quite replicated since. Combat was probably the most fun part of the system. The Monster Manuals had lots of tactical options for nearly every race of monsters, which the 5e manual just lacks (which is why I'm converting my 4e manuals to 5e).
- You couldn't make a character sheet without that awful Silverlight app. We briefly tried just using books, and it was just too much of a pain in the ass. At $75 a year, the DDI app felt like a total rip-off, and I'm glad to be rid of it. With 5e, it's still best for casters to use cards rather than the book, but you only buy those once, and I prefer to buy an attractive, physical product rather than a digital app.
- The monsters all need heavy adjustment. Without reducing monster HP and increasing damage output, a single 4e encounter was always a 2-hour slog. And, of course, it was easiest to do this using the DDI app!
- I spent too much time staring at my computer. So much needed to be done in-app that 4e eventually made it feel like buying the books was a waste of money other than giving the players something to read when they planned their next level. As the DM, I spent a lot of the game hunched over at my laptop, clicking through the monsters I had saved in the app.
- 5e doesn't need a sheaf of house rules. 5e is the first version of D&D we've played RAW and not had to make major adjustments. By the time I'd dropped 4e, I was removing the +1/2 Level slider from everything, had a list of banned feats, and limited OAs to one per round. It made the game more playable, but also slower to adjudicate. 5e...has no +1/2 Level slider, very few feats, and has bonus action/reaction/concentration rules that put fundamental limits on things that stop major imbalance before it happens. So to a large degree, it implements my 4e house rules already.
- 5e's the cleanest, best-tested D&D ever. 5e is just so well put together that it's hard to want to go back to any older edition's flaws. It's that simple. It's so much harder to break, and the rules are so much more streamlined, that the older editions really are not worth going back to now.