I started DMing again this fall after a 14 year hiatus, which, other than a couple of one-shots and a failed attempt at starting an FFG Star Wars campaign which only lasted for a single session. I've now got a group of five regular and four occasional players who meet for five hours two Sundays a month, and it's going absolutely great!
What's changed:
1. I no longer game with complete wangrods and challenge them to an armsrace.
While I look back with fondness on my high school games, the truth is my players were a herd of jackasses. Most of them are still close friends to this day, but the way they gamed back then left me scarred for years. The way they could find options and tactics and persuade me to make rulings that utterly broke 2e was brilliant in it's exploitativeness. This lead to an armsrace - I'd pour over Combat & Tactics, not to amp up my NPCs, but to rewrite and rebalance the game. I'd start new campaigns with new rules, trying to give players as much flexibility as possible... and they'd use that flexibility to construct monstrosities. Occasionally this backfired on them (like the guys who thought making an evil Necromancer and Cleric both with a 3 CHA was a smart idea, and found their characters burned at the stake by the end of the first session), but often they'd clean my clock. After the session where the 5th level Paladin with the Berserker kit and 18/97 Strength (YES, I ALLOWED THIS) managed to kill the main campaign villain in two rounds with his BARE HANDS, and I walked out of the room in dismay, I vowed to never let my players push me around again.
Since then I became obsessed with making sure I knew the rules inside and out and had balanced, official rulings on everything.
But then, in one of the last campaigns I ran during college, one of my friends pointed out,
"Dude, when your game is on, it's on. You have moments of greatness as a DM. But most of the time you seem more obsessed with the numbers than the game."
After that campaign I didn't run a game again for years, but when I returned to DMing, I took it to heart. I got over my wangrod-gamer-PTSD, and found that when playing with mature adults, such obsessiveness is not necessary. So I've dialed down my worry. I also love 5e because it isn't filled with the sort of niggling optimization that started with 2.5 (Player's Option) and reached it's zenith with 3.5; it doesn't punish players for not understanding how to optimize their characters, but isn't filled with builds that are utterly broken. I'm sure there are ways to break the game at high levels, but I have a much better idea of how to deal with that now.
2. I'm running a game, not writing an epic.
My earliest campaigns were attempts at writing novels; they were railroad, filled with attempts at replicating my favorite novels and movies... and broke down because of it. In fact, I realize now that this mentality only fed into the "arms race" above - trying to wreck my plans became the main goals of most of my players, who started to get their jollies from "beating the DM".
Now I just go with the flow, and go the way the players go, letting the game unfold as it may. I have no particular attachment to my villains, or to any particular heroes. The story is what we make of it at the table.
(Matt Colville had a very good video on this, re-imagining The Hobbit and the Lord of the Rings as two D&D campaigns run by a teenage boy a few years apart. The first, The Hobbit, was a game - fun, sandboxy, and unexpected. The second was overly planed, overly detailed, and railroad - but a whole lot of fun for the players who decided to wander off-script and make it their own (The Aragorn player and his murderhobo buddies playing the Elven and Dwarven fighters), if extremely dull and frustrating for the ones who found themselves locked into the story (particularly the Frodo and Sam players))
3. Serve the Players
There's no one right way to play. All of the player types identified in Robin's Rules are cool, and fun to play with if you give them what you want. I have no preference.
Equally, I no longer try to be extremely restrictive. I give guidelines, but if players have a cool idea that steps outside of them and fits the setting, I run with it.
4. Simulationist? Narrativist? Gamist? It's all D&D to me...
As I noted above, I started my DMing in high school as an obsessive narrativist running 2e (and a number of other games, including Star Wars and Earthdawn), and in college became an equally obsessive simulationist running 3e/3.5. I was trying to make everything fit together and logically cohere, and obsessed over details that didn't matter one bit to my players. Naturally, I hated 4e when it came out because it threw out all my crazy simulationism.
While I still don't care much for 4e, I no longer hate it for throwing away my simulationism, as 5e isn't particularly simulationist either. I focus on running the game. To make everyone - including myself! - happy, I need to emphasize all three at different times.
But it's all D&D to me.