I have a 4 year old Old English Bulldog. He doesn't have breathing problems, but he does snore a lot. You have to make sure you clean out their facial wrinkles, especially the ones that drain from the eye. My bully had itchy skin problems so I started giving him Brewers Yeast tablets and higher quality dog food.
Bud is good with the kids, and my cat, and my ferret. He doesn't mind most things. Well, he doesn't like my neighbor... but he likes my neighbors wife and 20 month old daughter. When someone wrestles, or slaps each other he gets upset about that, and he's bitten (not hard) the people scuffling. He doesn't like that sort of thing to go on. When someone knocks late at night he sounds viscious (sp?) and I wonder if he might bite when challenged by someone. He has nearly bitten my neighbor because he pesters him sometimes... but Bud is a far far cry from what I'd call a "mean dog".
Over-all, owning a bully has been pretty nice. He's a very personable dog.