Oh yeah, two players through the exact same rig will sound different for sure...
I really became aware of that when i played through Angus Neal's rig (flyangus from this forum). He was playing through it and he has this total EVH vibe in his playing, and he tends to sound like that no matter what rig he's using. As soon as he passed me his guitar and i started playing, it sounded totally different.
I then hooked him up to my rig, and same thing happened. His tone was there.. and as soon as he passed me the guitar, it totally changed.
Many things affect the tone, but I put a lot of it down to the player's pick attack. Obviously many other factors come into play, but i think the pick attack is one of the main things that sets us all apart.