The gameplay is significantly improved from the first game but the other aspects are worse.
Luigi has a lot more options in his toolkit allowing for more interesting puzzles. Suck, blow, flashlight, darklight, jump, plunger, etc. are more interesting mechanics than the generic fire/water elemental puzzles in LM1.
I played the whole game co-op which was really fun. Luigi and Gooigi had different difficultly levels so the player that's better a games can take Luigi, but the Gooigi player still has unique abilities that won't make the second player feel left out.
The bosses don't have dialogue or much personality anymore. I miss the little backstories they had. Likewise, the music is fine but doesn't have any iconic tracks like the original Luigi's Mansion theme. The graphics and animations are still detailed though, but rather than any genuine horror the game relies more on slapstick comedy.
While LM1 was short, charming, and simple, LM3 is a longer experience with significantly more depth and complexity. While I ultimately prefer the later it didn't need to sacrifice what I liked about LM1.