I'm far from an expert - I have owned two bull terriers though, and learned a lot while volunteering for BT rescue for a couple of years. So this is largely opinion based.
I don't really know what types of work APBTs are used for, so it's hard for me to answer that question overall - bull terriers are very strong physically, but if they don't find something fun, it's very hard to persuade them to do it for long. Someone told me once that trying to get a BT to do something it doesn't want to do is the equivalent of pushing a chain, and that always stuck with me. Because they've been bred as a companion animal and not a working breed, any qualities that would enable them to perform certain tasks are there by default, not because they enhance a particular job the dog was bred to do.
Generally, BTs make terrible "outside only" dogs. They are really needy, they get bored very easily and they need supervision. If they aren't getting enough attention or entertainment, they will seek it out - they will figure out how to climb or dig under fences and run away, they will throw themselves at strangers for attention and/or affection, they will chew on rocks or chain link fences until their teeth are nubs, they will develop obsessive behaviors. They don't tolerate extreme temperatures, hot or cold, very well, another reason they're not good candidates to be outside dogs. I don't have any statistics to back this part up, but my dogs, almost every rescue I've seen, and so many BTs I've heard about on message boards and such have been highly sensitive or allergic to insect bites of all types (fleas, mosquitoes, flies, etc.), another factor that's harder to control if your dog stays outdoors for extended periods of time.
(I have always been concerned about the possibility of my dog being stolen which is another reason I don't leave him outside when I'm not at home or can't check on him regularly. And with the level of freak-outs and overreactions that can occur in the general public, I really would hate for my dog to get out and approach someone who misunderstood his intentions. Just within the past couple days, I saw a report in the paper here where a cop shot 2 supposed pit bulls who allegedly attacked a jogger - as I read the article, it didn't seem that the man was even bitten, a dog may have knocked him down and I really wonder if that's what happened. So those aren't necessarily reasons that BTs or APBTs specifically don't make good outside dogs, but reasons that it might be better for them to be inside dogs, if that makes sense.)
The breeders who are really committed to the breed have done wonders with the overall temperament and dog aggression has been greatly reduced. Of course, there are some crappy breeders out there and people who don't socialize their dogs properly so it hasn't been eliminated - it's probably impossible to say you can completely eliminate it due to factors that breeders can't control.
Prey drive seems to be a very individual thing - I suppose that it may run in families. My first dog was fine around tiny creatures of any type - he would chase a cat if it ran but had no evil intentions when he caught up with it, several wild critters survived very close encounters with him with no harm done. On the other hand, Luke thinks if it is small and furry or feathered it needs to be grabbed and shaken as hard as possible (although he is absolutely fine with very small dogs, like my in-laws' 7 pound Maltese and 6 pound shi tzu mix).
So, that's what I know in my more limited experience - maybe some owners of multiple BTs will weigh in with some more info, too.