I'm not sure that there are differences between characters in those genres. Certainly there are guides that say so, but that doesn't make it true. I personally prefer playing as a bigger character on Dragon Drop, because if I'm playing as Crash for instance, if I'm near the front and a big character is near the back, then I can't see myself easily on the screen. However, that's not a character strength issue.
In Ballistix, everything depends on your own reflexes and the hovercraft moves with the same speed for everyone. In Pogo Pandemonium, it doesn't really matter with which character you are going to play because all of them move at the same speed with their respective pogo sticks, springs, jet-packs, etc. In Crash Dash, it is easier to win the race if you keep the hovercraft closer to the inner circle of the track and continue going around it. That way you get an advantage against the others not only because you cut the turns better, but also the chances of not getting hit by a missle increase. Finally, for Medieval Mayhem, particularly for Ring Ding, Crash is the best choice because you can use his spin move for two things: gaining a little boost of speed and when you have the vacuum cleaner, you can repel the enemies before they hit you and still pop the balloons simultaneously. You can do the same thing with Coco but Crash's spin is more effective. For the rest three medieval-themed levels, every character is equal.
I'm pretty sure I can remember getting around more quickly as Dingodile in the Crate Crush levels than I did as Tiny Tiger. I may have found Tiny to be better at throwing, but then I've never been that good at throwing crates anyway so it wouldn't really have made much difference.
I was never that good at spinning the crates either, so the computers usually beat me at the start of the Snow Bash game when I raced to spin or throw the crates at Penta Penguin to wake him up and send him wreaking havoc for the other players.
I don't recall Dingodile being the best character at pushing in the Polar Push games which is surprising since he's a large character so I'd expect him to have better pushing strength. It's been a while since I last played the game since I don't own the game or a PS. I should consider getting in touch with someone that does own the game and does have a PS.
I did some testing in Pogo Painter (I assume the other pogo arenas would be the same but I could be wrong) and Thaswordster is right. Like C.Syde, I actually thought Dingodile and Rilla Roo had the same stats in every minigame, but they don't in Pogo Pandemonium.
All characters except Rilla Roo: 150 jumps in the 90 second time frame without speedy boots, 24 jumps in the 8 second speedy boots interval.
Rilla Roo: 159 jumps in the 90 second time frame without speedy boots, 26 jumps in the 8 second speedy boots interval.