Oh man, I love Super Mario Bros 2! It’s one of my favorite games of all time.
So, each character actually has very different stats.
Luigi and Princess have obvious special jumping abilities. I think Luigi can actually jump a little farther… But both of them have significantly shorter jumps and run more slowly when carrying a vegetable, and both pick up vegetables quite slowly (especially the princess). This can be extremely detrimental on sand stages that require a lot of fast digging to get away from enemies, or picking up a block to throw at a boss before he attacks.
Toad is the opposite. He can pick up vegetables and run with them blazingly fast, and can run and jump as high (higher?) while carrying them.
Mario is balanced all-around.
It’s all explained in the instruction manual with some cute drawings. Each character is really quite balanced in my opinion.