So for the most part I play one of two games, D&D 5th and the Narrative Dice system (either Star Wars or Genesys). Both use experience points but in different ways.
In D&D you get earn a chunk of XP then spend it on a level of a class, which gives you a package of different abilities depending on the class. You get some Hit Points and maybe spells, new abilities or extra attacks. This feels good because of everything you had to do to earn it. However, it does feel... mechanical. I killed fifty goblins, now I know how to cast Fireball! It sometimes doesn't feel earned.
In Narrative Dice you get XP at the end of every session. This allows for character to make small improvements over time in the direction the character wants to develop. But this has a similar problem. "I spend my XP on three skill ranks in Medicine and two tiers of the Surgeon talent. I is now a dOcTOr!" In a typical game, that would take two to three sessions of worth of play.
These two games represent (in my opinion) the majority of leveling systems in TTRPGs. Most games have either the Level Package system or the Piecemeal/A La Carte system. I've only ever played in one game that didn't use either and that was Burning Wheel by Luke Crane.
Burning Wheel's advancement mechanic was simple...ish. The more you did something the better you got at it (in theory). You earned (Dice manipulation) points at the end of each session if you role played your character hard enough and the other players agreed. You would then use them to help you pass tests to help improve your skills. It is an excellent game system for medieval low fantasy. The kind of game where fighting should be your last opinion because recovery from injury takes days and weeks, not hours. I highly recommend it if you can wrap you head around the rules. Its a DENSE system (again, in my opinion) and I've covered it in very broad strokes.
I will look up Burning Wheel, that sounds interesting :)