Is this looking back after the fact, and making your decision, you making your decision completely in the dark? If it's looking back, then I'd have to say I'll take the 10 years of competitive teams because then at least you can look fondly upon the last decade of good to great teams falling just short. However, if you're talking about completely in the dark, give me the championship every single time. That's what sports is all about, and having the euphoria of winning a title lasts a lot longer than just one single season.
It depends on the sport. If it's football, I'll take 10 years of competitive teams. There's nothing like waking up on that Saturday/Sunday morning of a big playoff game. Seriously, I can't even remember who won the Super Bowl just three years ago.
As long as being competitive means a chance at a championship (i.e. not just winning a crappy division when everyone knows you have no chance), I go for that.
