The main things to know: XBOX is the fastest version

GC is around 2 mins slower in any% PS2 is around 7 mins slower in any% (all in terms of load times)

PSN has loads which are slightly slower than GameCube (the game is only available on PSN in Europe)

(the time difference is smaller in NG+ and larger in 100%)

As for backwards compatibility, PS3 should be like PSN with loads inbetween PS2 and PSN (the game should work fine on both hardware and software emulation BCPS3s), Wii is a tiny bit faster than GC and the game doesn't work on XBOX 360 (excluding modding the console).

As for version differences, All consoles are mostly the same from what I gather in terms of gameplay although there are two notable differences.

The first difference is in Ambush Grove. On XBOX, you can hit the rockers anyway to damage them while using the cannon which makes the one cycle Ambush Grove much easier. On GC and PS2, you need to hit the rockers in the center to damage them, or they will simply flinch without taking damage. This makes one cycle much, much harder on these versions.

The second difference affects 100%. On XBOX and PS2, if you save the game while in a level and restart the level, you get to keep all the bugs, crystals and fruit you've collected but on GC, you don't get to keep all those things. There is a way around this but it's very slow. When you have collected all the stuff you want, you must enter the portal for the next area. Once you have done that, you can then save the game. Once you have saved, you must quit the game and reload the file. Once you've done that, you can then restart the level with all the bugs etc. collected. This makes grinding way slower on GC which means that you must collect a lot more items during your run so you can decrease the amount of grinding needed which also loses time as you're going out of your way to collect more items during the run. This also makes setting up an NG+ file more of a pain. GC would still be faster than PS2 in this category though as load times should definitely make up for the time loss but it's still much slower compared to XBOX. As a sidenote, XBOX takes longer to save than the other 2 versions but it makes up for it with its load times (and this is only really a factor in 100%).

As for some smaller differences, on GameCube and XBOX, walls cannot be seen Out of Bounds, allowing you to see inside rooms from Out of Bounds but on PS2, the walls can be seen from Out of Bounds. This makes Out of Bounds navigation in some areas harder on PS2 since you can't easily see where you need to go. On PS2 and XBOX, you can use the analogue stick or dpad in the pause menu but on GameCube, you have to use the dpad.

PSN suffers from extra input lag which naturally makes this version more inconvenient/frustrating, especially since it is the PS2 port. Pause buffers can be stupid on XBOX if you are using an original controller, particularly the controller S with its start button below the left analogue stick. This can be worked around by using a different controller. PAL and NTSC are pretty much the same.

To further add on, an XBOX with a Samsung disc drive is the fastest (the later Samsung A disc drive is better from what has been tested). The main thing that affects loads on XBOX is the actual disc drive itself although the difference between a good disc drive and a weaker disc drive for the most part is fairly small. The best way to get an XBOX with a Samsung A drive is to buy an XBOX with a manufacture date of 2004 or above.