I'm thinking of printing up tons of BM and having a huge throwdown. Are they fairly balanced between sets?

There are some that are definitely better than others. Here are some that work very well together:

Soldiers
Vampyres
Brom
Lunch Money
Legend of the Five Rings
Fantasy
Samurai
Club Foglio (XXXenophile + Studio Foglio)
Dork Victory
Brawl + Origins 2001 promos
1999 Promos: Eiko, Wu Lan, and Zeppo
(Fightball and Nodwick should also work well, but I haven't tried them myself.)

Try to stick to tournament legal buttons and you should be fine.