Hmmm...I'd actually say the in-battle EXP bar underneath the HP bar. No, seriously, hear me out. Go back and play the first generation games (if you can stomach it) and see how utterly infuriating it is to have to constantly check each individual Pokemon to see how much EXP it needs to get to the next level. See how much time you waste doing that. It's the smallest, most trivial of things, but it makes such a huge difference to not have it there. Sometimes I actually forget Gen I didn't have it.
New features in Pokemon have come and gone over the years, and whilst a lot of them have made a bigger impact on me, they haven't lasted, because Game Freak are a bunch of cun[? SKELETON WARRIORS ?] and keep taking them out. I love following Pokemon, day and night, upgraded Pokedex features like DexNav etc., and all that other stuff as much as anyone else, but they never last. Super Training was a thing I loved and would have said if Sun and Moon had kept it, and I'd LOVE to say Trainer Customisation but it's so painfully minimalistic and unsatisfactory that having it there actually feels like a slap in the face sometimes...and it could always get taken out with the next games anyway. All of the features I've liked have drawbacks, in that they're exclusives.
Wi-fi changed things a lot for me, but only for Gen IV. The physical/special split made the games more interesting strategically, but has actually put me off using a lot of Pokemon or giving them certain moves - I'd love to use Sharpedo in ORAS, but teaching it Surf would be a wasted move slot, meaning I'd need a HM Slave for it, so I won't use it. I think in terms of time saved checking menus constantly, lasting effect throughout games, and just general convenience, having that little blue EXP bar changed things the most for me, and has made the games that much easier to play over the years.
I don't wonder any more how much longer I have to wait until my Pokemon will level up; it's reassuring, having it there to tell me, so I can gauge how much more I have to do until I reach the next level. For someone who plays a lot of JRPGs that don't have anything like that, it's made a world of difference to me, especially when I haven't had the motivation to grind in a lot of Pokemon titles. "Just [x] more battles until the next level" is something I've said to myself more than once, and watching it progress is satisfying even when it's frustrating just how little it crawls up.
So, yeah. It's the small things that make the biggest difference sometimes.