I don't know much about Staffordshire Bull Terriers, except their cute. I know they are supposed to be great with kids ("the nanny dog"). I sure prey drive would be a concern. Are you looking to adopt or buy? I personally, would try to find an older puppy or young dog so you can gauge it's prey drive. I'm sure it can work, though.
It depends on the individual dog as well as the training you do training. I'd discuss it with the breeder and find out if their bloodline is excessively prey drivy in general before making any decisions.
Patch O' Pits , Home to Greatly Loved Ch GRCH, Therapy, & Agility APBTs "When it Rains Play in the mud"
I have one whom I would not trust alone with the cat for a minute. He has become used to the cat so that he doesn't charge after him on sight, but I definitely don't put it past him to treat the cat as prey. But I have known people who have had no trouble at all with their staffy and the cat. My friend's pit bull lived with me for about 2 years and he was great with the cat. He would bounce playfully up to him and the bounce backward when the cat reached for him. Terribly cute!
"Be who you are and say what you feel. Because those that matter, don't mind...And those that mind....don't matter."
It's up to the individual cat as well though, our Siamese HATES our staffy and Bull terrier, spitting, hissing and swiping at them, our little tabby however struts up to them demanding kisses and sliking through their legs to eat from their food bowls - she's shown the dogs that although small, she has no fear of them and i think they may even like her for it. :)