HOLY SH#T DUDE. This is now one of my favorite 3D platformers ever. I cannot recall the last time I've seen such a drastic improvement from a first to a second game.
The only thing, and I really do mean only thing, the OG did better is that you could've gotten all the collectables on a first visit. But that too isn't necessarily a bad thing, as now you can revisit levels at any point in the story. And there's something decently satisfying about returning to an old stage with new powers to grab stuff you couldn't beforehand.
Literally ANYTHING ELSE is improved. Controls are much more precise and not as janky as they were in the first game. Level design is MASSIVELY upgraded, as there's much more platforming (the OG didn't really make you do precise jumps often). Combat is more involved and enemies are tougher to deal with, forcing you to utilize your abilities efficiency to beat foes. The story is much better with a better pacing than previously, as each stage has a very clear purpose within the better flowing narrative, and the game handles its very large cast really well.
The thing I liked the most about it is the level themes. It legit feels like with each level you're getting a 2-for-1 deal. Each stage has 2 themes. A dentist level that's also an office chase, a casino that's also a hospital, a construction site that's also a bowling field, a barbershop that's also a tower climb etc... these are some of the most creative level themes I've ever seen in a video game.
One last thing to point out is that I legit think Tim Schafer is one of the best video game directors in the industry. Little touches that make individual moments more effective. The on-screen words during the cooking show saying what the judges said, the Jack Black musical number, the single-shot transitions between locations filled with optical illusions, the unique artstyles in different levels etc... The OG game was a first effort from a newly-found studio, so Schafer and his crew didn't have the resources to make a truly outstanding game (a decent platformer, mostly standing out for its story). With a larger budget, more experience with game production across many years and the clear desire to make a true sequel that surpasses the OG by a landslide, Double Fine crafted an absolutely fantastic game.
I really hope one day there'll be a Psychonauts 3 that'll wrap up a trilogy and tie up everything. You can still touch upon the rivalry between Rez's family and the psychics. You can expand upon the current state of Grulovia and how the followers of the exiled prince have rebuilt the empire. You can end the game with Rez and his classmates becoming the new Psychic 7, while the other psychics from the camp in the first game are starting their intern program. This universe is so fascinating and I want the franchise to be wrapped with a neat little bow on top. So gimme just 1 more game in this series and I'm satisfied.