This is some quick info on which versions are faster for which categories and also "version differences". I will first list off the region differences that are relevant to explaining why X version is faster for X category and then list general region differences that are still relevant to the speedrun

REGION DIFFERENCES

FASTEST FOR ANY%: NTSC-U (North American version) Reason(s):

• On J you cannot skip the box cut-scenes at the end of levels. On U you can death abuse after a checkpoint to make it not load at all which is faster most of the time than watching 1 box fall on crash's head. This death abuse also kills two birds with stone as dying resets global cycles, so by choosing to death abuse on the checkpoint that gives the best cycle positions, you save even more time.
• J has RNG delays in the box cut-scenes which can make you lose time by screwing up global cycles you try to carry through levels.
• Note that J is faster for TAS because it can get perfect box screen RNG which allows it to viably map out a fast full run cycle and also it doesn't have to setup zip-zagging (TAS only movement tech) again each time after death abusing.

FASTEST FOR 100%: NTSC-J (Japanese version) Reason(s):

• Road To Nowhere only needs 1 visit instead of 2 because the red gem (which is needed to reach the secret boxes) was moved to The Lost City which is before Road To Nowhere instead of after it.
• The death abusing stuff mentioned for any% doesn't matter much in 100% here since you get gem screens on most levels anyway.

PAL (European/Australian version) is very slow and very different

OTHER RELEVANT REGION DIFFERENCES (using NTSC-U as the base comparison)

PAL:

• 25 fps instead of 30
• Crash's base movement speed has been increased (don't be fooled into thinking this makes this version faster).
• Crash's jump height has been increased
• Zigzag has a higher threshold to meet for it to save more.
• Slower loading times
• Slower animations, map transitions, bosses, cycles, and more
• Desyncing cycles in Sunset Vista, can death abuse at the start to fix this on J, not sure about PAL.
• Different method for Cortex Power skip is available here.

NTSC-J

• Password can only be accessed by inputting this code at the title screen: UUDDLRLRLRO
• Added hints to some masks where a text box will appear and kind of "pause" the game. It can only be skipped with X or O, which will buffer it into a jump or spin respectively unless the mask was collected in the air for pressing X. A submarine jump with O can also be used to make surviving after skipping the hint easier. The placement of these masks work in a weird but understandable way - they will move based on which ones you collect in a level and if you die. For example, Cortex Power has 3 masks and 2 hints - if you skip the first one, the hint that shows after collecting that first mask will move to the 2nd one and the one that shows in the 2nd one will move to the 3rd one - so if you collect the first 2 masks the 3rd one will have no hint.
• Added some more Tawna bonus rounds (this is relevant due to added boxes, I will point out where these are). Interestingly, some of these new bonuses will not have tokens load in their respective levels if previous bonuses have been completed.
• 1 box falls on Crash's head no matter how boxes were missed and cannot be skipped by dying. Death abusing in NTSC-U to skip this entirely is still faster most of the time.
• You can now enter levels with O in addition to X
• To skip gem cutscenes, O and Triangle can be mashed instead of just X
• Triangle can be used to skip the save screen after bonuses
• You can die past a checkpoint and still get the gem if you backtrack, though this is not faster than re-entering anywhere.
• The boulder moves a bit slower on J, making "boulder skip" in Boulder Dash 2 easier.
• The 1st mask in N. Sanity Beach is collected automatically upon skipping the cut-scene at the start instead of being in a box, making this level a little bit faster in J for 100%
• Platforms in Upstream and Up The Creek are larger, the only things notable about this is it makes it easier to not zigzag off the side by mistake, changes double jumps positioning, and makes some strat in the orange gem possible (or more viable idk haven't tested on NTSC-U) when not doing upstream skip.
• If you die in a boss you will respawn with only 1 mask (wtf lol) - if you die on Ripper Roo you should re-enter.
• Papu Papu has two more hit points - he will move faster for each one
• Green gem has been moved from The Lost City to Hog Wild - this is not enough timesave to make NTSC-J faster for any% in RTA
• Added box above the 1st TNT near the start of Temple Ruins and at the end for the bonus round.
• (again) Red gem has been moved from Slippery Climb to The Lost City.
• Sunset Vista has been swapped with Slippery Climb (reason is that they thought Sunset Vista was harder so they wanted it later). One issue this causes is desyncing cycles - they are easy to deal with in Slippery Climb, and easy in Sunset Vista as long as you death abuse at the start to reset them (which also makes them faster, wow!). If you don't reset the Sunset Vista cycles they can be a nightmare if they desync.
• Sunset Vista cycles can break if you die past a checkpoint and become hilariously slow, however this is only an issue if for some reason you are running any% on J, it doesn't seem to happen in 100% after re-entering)
• Added a box near the end of Cortex Power for a bonus - this becomes a checkpoint after completing the bonus round/completing the game 100% which is very useful for practicing the exit part of the skip!
• Added mask near the end of Toxic Waste, slower to get anyway
• Removed metal crate above the topmost TNT near the end of Toxic Waste - this means that on J you must bounce on the top TNT to make it break off-screen, while NTSC-U doesn't have to as the metal crate landing on it will begin the countdown after breaking the middle wooden crates.
• Added mask at the start of The High Road, slower to get anyway
• Shorter High Road, it ends about where the 4th checkpoint is in NTSC-U
• Added some boxes in Slippery Climb, doesn't matter much
• Added mask to the start of Slippery Climb - doesn't matter much since island 2 is filled with masks but it can be picked up without timeloss besides the pause from the hint if the starting cycle is bad
• Added checkpoint near the end of the 1st floor in Slippery Climb - just means you have to re-enter if you die past it on J
• Added mask at the start of Jaws of Darkness, makes the respawn cycle here possible which can save around 10s sometimes if the global cycles here are bad
• Added some boxes to Castle Machinery for a new bonus, doesn't matter much

VERSION DIFFERENCES

There are none! Enjoy your non-existent headache over this. No 1.0/1.1 crap, etc.

There were different labels released like greatest hits for NTSC-U and like 6 different labels for J (lmao) but none have any in-game differences.