In theory, bankroll size for tourneys?

I friend and I were having a debate on how much one should have for a bankroll playing in mostly tournaments. With limits, people say somewhere between 300-500 big bets, which would make about 10 sessions or so. Anyhow, should bankroll for tournaments be the same i.e. if I play $10-1 sit and gos, should I have about $110 (10 buy ins) or should it be higher since it's a tournament? I find myself doing well at this level and tend to get in the top 3 a majority of the time, so there are not a lot of times I don't win something, but there are still those times obviously. Thanks!