Final Fantasy X is my favourite in the franchise and easily one of the best games I've ever played, so that's my clear choice. Shenmue II is also amazing, and very unlucky to be released the same year as FFX, as that too would be a worthy personal winner.
2001 was an awesome year for everyone though and GTAIII, Halo, MGS2, or even Smash Melee would all be worthy winners. This is definitely the decade where my gaming tastes tend to divulge from the general public's the most, so I don't know if I'll be in favour of any of the vote winners, but we'll see.
One thing to note about GTA3 is that it isn't really that great. It revolutionised gaming, without a doubt, but San Andreas is where to franchise got good imo