Pretty torn up on this one.
Having owned a 64 since it's debut, I have quite a collection of games with it. Banjo-Kazooie, along with its sequel, has its place in that collection, and I've grown up with those games. I've had a blast playing Banjo-Kazooie and thought it was a great blast. My mother, who is iffy on video games, got hooked on the Banjo games and thought they were loads of fun. The story mode was enjoyable, the characters were brilliant, the graphics amazing, and...ok, every damn thing about the game was nothing short of amazing.
Dead Rising is another favorite of mine. Who doesn't want to go into a mall during a Zombie apocalypse and bash a zombie with an outrageous assortment of weapons and gadgets? Dead Rising's story and multiple endings were enjoyable, the characters were insane, and the graphics were pretty damn good for 2006. The game also received a Platinum Hits status and spawned itself an equally amazing sequel. The Psychopaths were all...well psychopathic in their own clever way, and the boss battles--while sometimes ridiculously annoying--were enjoyable.
Both games are great and it's pretty hard to vote...but since it's been with me since my childhood and remains one of my favorite games, my vote goes to Banjo-Kazooie.