Bull terriers are really a lot like many pitts but generally have a lower center of gravity and smaller. Just as powerful, tending to dog aggression (what they originated for ) and high prey drives. Any I have known tended to be boneheads and throw temper tantrums if they had something else in mind when you asked them to do something.....and two of those owners worked theirs in agility and obedience. (with
PR training- one owner is one of the best local trainers) .
Minis tend to be a bit sharper and less patient, though you might find a mini with patience. Like Crio said....They are higher energy than you might think and definitely not to be trusted with anything they would preceive as prey. They are terriers that need to be doing something,or get bored and destroy stuff. I wouldn't get one if you have to be away to work all day. You would want to put a lot of time into one training or you would hate each other. They are not really aloof but they love their family and other people are secondary.
Around here they are hard to find, pricey and some lines have kidney issues. Obviously the whites can inherit deafness.