For the PC:
Respect level "heads" and different ammunition numbers are from the beta. The cop cars just seem to be a STY replacement (so not an official GTA2 picture - probably taken by some GTA2 fan who modded the cop car).
For the PSX:
The PlayStation 1 had considerably less processing/graphics power than PC's could do when GTA2 first came out (I know, I had GTA2 for both PSX and PC!). They had to make graphics use less colours, change the actual script files to generate less traffic, objects (classic example is there is only 1 crane per city in neutral area in total on the PSX compared to three cranes per city in gang areas only on the PC) and even change mission code itself (on the PSX, an example would be instead of making a new car, there is a PSX specific car that guarantees the specific car type to drive along near the player when it's called). Also, PSX maps had no lights, and thus, no dusk mode option. I don't have my old GTA2 PSX disc any more so I can't check!
Oh yeah, apparently PSX GTA2 didn't have trains enabled on them! PC and DreamCast did.
Not sure why the armour icon is in a different position, but either had issues with screen resolution (unlikely - although PSX game resolution is pretty small) or the display was built specifically for the PSX version. Who knows? Rockstar knows
As for the Game Boy Colour, never knew it even existed! At first I thought it was a custom job, but no, apparently it was officially released on the GBC in 2000!
Can't blame it for looking pants though, although the interface reminds me a little of the classic Doom