The N64 offers a wide variety of platform games (which happens to be one of my favourite genres). Games like Super Mario 64, Donkey Kong 64, Banjo Kazooie, Banjo Tooie make this a clear winner personally. Games like Ocarina of time help out too.
PS1, I'm sure, is a great system, but nothing will ever come remotely close to Banjo Kazooie or Ocarina of time.
Lyrics: He He He He Ha Ha Ha!