There are quite a few differences in each version and here's a rough outline of them:

XBOX: Possibly the best version of the game to run (at least for full game any% runs). You have to wait 2 seconds to skip cutscenes unlike the other versions or more depending on load times after skipping the cutscenes unlike all of the other versions but other than that, it is optimal as all skips work in this version.

Load times vary from console to console although as far as we know, a Samsung A drive is the best disc drive for this game. In level cutscenes also have loads but these still load faster than PS2 and especially GC. One thing which is only in the XBOX version and is rather beneficial (at least for full game runs) is something called reverse lag. Basically, the game sometimes speeds up during gameplay when a lot of stuff is on screen. This can be annoying when slope climbing or generally performing hard skips but in general, it saves a whole chunk of time throughout the course of the run overall (the exact amount of time this saves will depend on the run but it will definitely save well over a minute in an optimal run. It also does not effect the in game time so it's irrelevant in ILs). Slope climbing is easiest on XBOX and PC.

Side note: The game is also 360 compatible in all regions. Level loads are a little bit longer compared to optimal XBOX models. There are a couple of graphical glitches and more importantly, the game has performance issues which slows it down overall but the game is pretty much the exact same otherwise so running on 360 while sub optimal, is totally fine.

XBOX HDD is also banned as it has noticeably faster load times than a normal disc (although this could be unbanned in the future if the game becomes backwards compatible with XBOX ONE/Series X in the future where it will likely be even faster).

PC: PC is a strange case. Load times in the PC version are really unusual because the game does not just load the level once the data has been loaded, like you'd expect. The game instead does not load the level until the model on the loading screen has rotated to a certain position, regardless of your PC specs. How fast the model rotates depends on the framerate and the framerate naturally depends on your PC specs. Most of the game tries to be capped at 60FPS but the load screens have a completely uncapped framerate, and capping the framerate does impact loading times. This means that moreso than a lot of games, how fast the PC version is entirely depends on your PC. Because of this, it is entirely dependent on your hardware whether PC is faster than XBOX or not in any%.

With a top end rig costing thousands, load times are very quick and the game can be faster overall compared to XBOX. On less powerful hardware however, load times are longer to the point where PC loses time overall XBOX overall. How much time it loses will depend on your exact hardware but even high end hardware from 2017 can struggle to compete with XBOX. Because of this, I do recommend XBOX for any% as while a powerful enough PC can surpass XBOX, a PC of that calibur will cost thousands and an XBOX is a lot cheaper.

The main plus however is when the game is played without the disc inserted. The CGI cutscenes do not exist if the disc is not inserted which saves a ton of time. These cutscenes do play when playing off of a PC disc and they can sometimes take a really long time to load which can lose a lot of time. You can eliminate this however by removing the disc from your PC while the game is running but this is not guaranteed to work with all PCs (or you could play a version you downloaded online). Another thing is that when the game is played in windowed mode using Dxwnd, the game will temporarily freeze during some load screens which can lose a decent chunk of time so try playing in full screen if possible (or use another method to play windowed). Camera controls are quite a bit faster on PC which could maybe be beneficial in certain areas. PC also has different swinging physics which can be beneficial in a few areas but there are currently no practical uses. One very useful thing for cheat% categories is that you can type in cheat codes with a keyboard on PC. This saves a decent amount of menuing, saving a bunch of time and opening up more opportunities to use cheats in full cheat% runs (although it doesn't affect in game time so ILs are unaffected).

This may be possible with a USB keyboard on PS2 or a keyboard adaptor for XBOX/keypad for 360 but this has not been tested yet. There is also a strange detrimental glitch in the PC which can happen in the Dash levels where Dash keeps going in and out of the air. It is currently unknown what causes this and it may not be an issue for you.

For any%, a comparison between XBOX and PC is difficult. With an optimal PC setup, PC will save close to a minute from cutscene skips but XBOX will save that time back from reverse lag. The difference still needs more extensive testing. As of May 2020 with all the available PC runs, Lexos has the fastest PC loads, followed by SuperSqank by a decent margin (a close to 20 second difference) and then followed by AceTheDolphin guy by a little bit and then other PC runners by a noticeably larger margin. For cheat% categories, PC is superior due to the ability to type in cheats. For ILs, PC might be more optimal due to the faster camera and the lack of reverse lag although this is very minor. XBOX is perfectly runnable for ILs, especially as not all ILs have been fully optimised yet.

PS2: Slowest level loads although in level cutscenes load faster than GC, slope climbing might be harder and the skip in Robot Arena is not possible. Mostly similar to XBOX other than that (apart from the lack of reverse lag). There are a couple of weird differences which don't effect the run on PS2 such as the muffled sound effects and a couple of insignificant things were patched which don't effect the run.

PSN: same as PS2 but with much faster loads. The loads are still slower than XBOX and it suffers from the same issues as the PS2 original. BCPS3 has loads inbetween PSN and PS2.

GC: Hardest slope climbs, cutscenes take forever to load the next section and here's a list of skips which don't work: Bank Heist cutscene skip Appartment Inferno skip (Technically works although it is way harder and the slightly slower backup done in the IL WR is also quite tough) Robot Arena skip Standing on the claw in Finding Mr Incredible (OOB is still possible and you'd do this exploit to make it practical ) Some other skips may not work however, they have not currently been documented. Various skips are also a lot more difficult mainly due to harder slope climbing. There are also various smaller things which are slower or different on GC which can make things harder. Some examples are that running up for a big jump in Bank Heist is a lot slower for some reason and some of the terrain in Skyline Stretch is different which makes the generator skips harder. GC also runs at 30FPS while the other versions run at 60FPS (Finding Mr Incredible and Rocket Silo do run at 60FPS though for some reason).

Region differences: NTSC-U has Miles Per Hour in the dash levels instead of Kilometers Per Hour in the PAL and NTSC-J versions. CGI Cutscenes are also 4% faster on PAL. Nothing that changes the run at least from what we're aware of for PAL and NTSC-U.

On XBOX, the PAL version of the game game is different when the console is set to PAL 60 or PAL 50. PAL 60 still runs in 50hz at a PAL resolution however, the overall look of the game is different to PAL 50. It’s currently unknown if this makes a significant difference.

NTSC overall has faster loads than PAL, with PAL losing around 8 seconds to level loads (Other loads within levels have not been tested). NTSC has more reverse lag in some levels, saving time (notably Late For School and Violet's Crossing) but I think PAL might have an advantage in other levels (I think Bank Heist is one of them). I do believe NTSC-U is faster overall but PAL is not far behind at all. It is definitely a completely viable version to run, even for World Record.

NTSC-J (at least on XBOX and PS2) is slightly different. Bank Heist cutscene skip and Crane room skip in Finding Mr Incredible skip don't work which combined lose around 45 seconds. NTSC-J would be the same on GameCube since these skips don't work in any GameCube version.

PC or XBOX are the best ways to run this game and not have the hardest time. PC is more optimal in the cheat% categories as you can input codes a lot faster giving you more opportunities to use cheats. Unfortunately, the PC version is quite strange, especially with its highly variable load times depending on the system/setup as well as with the weird Dash glitch. This might make XBOX more desirable overall as while it does have variable loads depending on the system, it is nowhere near as severe as PC. If your PC copy doesn't have Dash skip however, it is still runnable. On PS2 and especially GameCube, you will make an already extremely hard speedgame even harder and you can't be competitive in the full game categories.