Indeed, I just watched both runs back to back and there's a flurry of superjumps that are used on Xbox only and save a considerable amount of time compared to the PS2 version. I mean, HHQ is basically skip after skip in the former. It even feels that the ones used in both versions are much easier to get on Xbox, requiring a lot more tries on PS2. Overall, this is maybe what makes Rayman 3 a slightly less interesting game to run compared to others, as most of the time it's just about getting OOB and heading to the level exit.
Not that there aren't interesting aspects to it though, I especially like how there's so many ledge grabs that were not meant to be possible and yet they are (maybe there's a trick I'm not aware of here?), and overlooked stuff such as the possibility to swim in the marshes far enough to grab the flying hooks.