I agree with Scott and Uglydog.
You find what you need in the apbt just do your homework.
And like Uglydog said...you will get all types in crossbreeding...and some of those will not look like either parent much less have the traits that you are looking for.
But if you want to do it then make sure you select the right pups otherwise you are just wasting your time or at the minimum will be a major setback. You want to have access to all the keepers with a verbal agreement that if the pup turns out right that you can use it a time or two for breeding.
If you want grit then both lines must have a ton of grit. The bull dog lacks nose and most have not been used as strike dogs so the strike dog has to have range, nose, and the ability to find a hog. Not saying that some bulldogs don't have a nose are hunt in them but the average bulldog is not bred for that.
if you just want rough running catch dogs these crossbreeds will work if they have a good strike dog to lead them around...all you have to do is pick the rough pups that want to follow a good lead dog. They just won't find many hogs if you leave the strike dog at home...