How can you tell which version of grand theft auto vice city you have?

Assuming you're referring to the PS2, there are three known versions - Original (earliest), Double Pack and Haitian-friendly (latest). The easiest way to find out is by doing two checks. The first is checking the names of the guns in the game, as these were changed for the Double Pack version.

Original (Double Pack/Haitian-friendly)

Colt .45 (Pistol)

Python (.357)

Spaz Shotgun (S.P.A.S. 12)

Ingram Mac 10 (Mac)

Uzi 9mm (Uz-I)

MP5 (MP)

Ruger (Kruger)

PSG-1 (.308 Sniper)

The next thing to do is check what weapon pickup is located behind the Washington Beach Police Station. If it's a tear gas grenade, then you have either the Original or Double Pack version. If it's a regular grenade, then you have the Haitian-friendly version.

Therefore if the guns in your game are named as they are on the left above, then you have the original version. If they appear as in the parentheses, and there's a tear gas pickup behind the Washington Beach Police Station, you have the Double Pack version. If they're as in the parentheses, but there's a regular grenade pickup behind the police station, you've got the Haitian-friendly version.

Have a look at RARusk's version changes FAQ at GameFAQs for a much more detailed account of the differences between versions.