I'm actually quite surprised nobody did this yet. I played the crap out of GTA 1 on PlayStation, and now I have it working on PC. Differences below;
The PS1 version has blurrier cars, and overall blurry textures,
-No parked vehicles in Liberty City (except for the vehicle side-missions)
-No trains (I sat there waiting for a WHOLE F#CKIN' HOUR waiting for a single train. None.)
-No Firetrucks, except for that one El Burro mission where you collect cars for him; there will be a rare chance of one spawning in traffic during the mission.
-All weapons/power-ups make the same sound when collected, the "Extra Life" collect sound.
-All sounds are lower-pitched and with reverberation, sounding a bit more realistic. <<<(this was just because of how my PS2 speakers were set up, it ain't true)
-The LC Porka Turbo, SA Penetrator, and Classic have different horns in the PS version, which sound very "clicky", almost like a truck horn.