I've kept several common snappers (C. serpentina) and haven't found them to be particularly aggressive, though all the ones I've had I got as small turtles, rather than wild adults. They are very "food aggressive" so I suppose you could get bitten by accident, while feeding. Ally's are said to be a little slower & calmer, but they're bigger so if it did get you you'd be in more trouble.
Actually now that I see you've kept softshells...my softshells were more likely to bite me than my snaps ever were.
Actually now that I see you've kept softshells...my softshells were more likely to bite me than my snaps ever were.

.... i wouldn't dare to put my nose near a snapper!!