Since I've only really been gaming for a decade this isn't a difficult choice.
My game of the dacade is also my favourite game of all time; Prince of Persia: The Sands of Time. I doubt anything will top playing that game for the first time, partially because it is an incredible game, but also because it's one of my first gaming memorys.
As for this year, it's a close run in with two games I would have never expected great things from: One is Batman Arkham Asylum, which is essencially a movie/comic tie in, which are almost never good (for exception see Spiderman 2). The second one is Assassins Creed 2, the sequel to a game which at best gave me cheap thrills and at worst made me angry.
I think ultimately Batman takes the prize as I got more game time out of it because of how much I LOVE the challenge missions and because it's freaking Batman.
So, GOTY: Batman: Arkham Asylum
GOTD and all time: Prince of Persia: The Sands of Time