I'm having trouble thinking of caveats I wouldn't want instead of a championship, or a title, or whatever.
I'd rather be Lance Armstrong, as played, than any other cyclist, ever.
I'd rather be Tom Brady with a ball-deflation suspension on my resume than any other quarterback, ever.
However, I think I'd rather be.....I don't really follow the sport...name a good baseball player. I'd rather be him than Pete Rose (most hits) or Barry Bonds (most HR's).