For fighting I don't know, but they were a sport dog back in the day used for bull baiting.
In reality I'd imagine the bulldog whipping a hound dog because of the fact they could hang with a freaking bull. The small compact size is an advantage for them, allowing them to get underneath bigger animals and attacking the throat.
Hate to say it, but UGA
The English Bulldog originated in the British Isles, descended from the ancient Asiatic mastiff. The dog was given the name "bull" because of its use in bull baiting and for their robust look of a little bull. They were aggressive, ferocious and courageous with the power to attack full grown bulls, which they did in arena combat before the practice was banned by law in the 19th century. The bulldogs would attack from the bottom up going underneath the bull and aiming for the neck, making it hard for the bull to fight back. Today's bulldog has a very different temperament from those of his ancestors, but still retains a strong determination.