If it's taking more than a full 60 seconds max then it could be a network issue, trouble loading your Live account and taking longer to boot. I sold my og 360 a few days ago and it was running tip top as well so its probably hit and miss from console to console. Hardware quality was a fail this generation.
360 does take longer to boot up though. Probably because the dashboard has a ton more crap on it than PS3's simplistic menu.