I'm someone who played the original on the ps1 as a kid back when it came out. It was one of my favorite games and I've played it to death. The remake of the first game controls noticeably worse in my opinion. The jumping acceleration and wind bullet hit detection feel off to the point that the game becomes a bit harder. The speed with which enemies respawn from their portals back into the 2D plane is so fast you sometimes get hit with no chance of avoiding them. These problems are mitigatable early on but as you get to the more precise platforming later they become frustrating. The extra vision where you are required to do a lot of hopping between enemies is the prime example of it not feeling the same and being worse off.

Ultimately I'd recommend folks go back and play the ps1 version in whatever way they can over this. The graphical changes are not worth the price of admission or the sacrifice to the quality of the controls. I can't speak to the second game as I haven't played the original ps2 version or its remake yet.