Is there a best character in Button Men? Is there a worst character?
(disclaimer: i haven't played button men seriously in ages, but i'll share my impressions from back in the day)

My feeling is that Lab Rats is the best button, as its 2-dice will allow skill-attacks on far better dice than it has to give away. Bunnies, with its 1-dice is also strong, but can too-often get trapped into not being able to make any attacks.

The worst by far has to be the dragon with d30s all down the line. Yes, it can take anyone's dice, but odds are you're going to roll one of them low, and give up 30 points at once. Do that twice and there's no way to win against most buttons.

Some are banned from tournaments for power. i think lab rats and bunnies were both banned at some point. Some are banned due to non-playability (how would you roll a pi-sided die for the James Earnest button?), and some are banned for their swingy nature (the xxxenophile buttons, with their 3 x-dice, were considered too "swingy"; you could completely change the nature of your button between rounds, though it looks like they're back on the permitted list)
http://www.beatpeopleup.com/tourname.html