Pits come in many shapes and sizes from nearly boxer size (little more stout) to monstrous dogs (easily 150lbs and 36" at the shoulder). I can envision a small pit being able to outrun and out endure a traditional gun dog breed - if the owner of the gun dog don't exercise the dog enough. But that is dependent on the individual dog. Like people, athleticism is dependent upon exercise.

I would question the desire. Take a random pit and a random (traditional) bird dog breed. Both never exposed to birds. Let both be trained by two equally professional dog trainers (like Smith brothers, Duffy's, etc.) - one on one with no other influence from other dogs. For the gun dog, how much time would it take from complete novice to finished gun dog vs. the same for the pit? Then take into account how long each trainer spends upon which aspect of training.

Now, consider the failure rate for each if both trainers trained a hundred random dogs (gun dog vs pit).

A simple Gedanken experiment (thought experiment) would be less failures for the gun dog breed but it shows how much is bred into the breed.

My setter is a wuss; She doesn't like dogs who are the same size or larger to sniff or approach her. Especially larger dogs. She immediately comes to me for protection. During hunting season, everything changes. She complete ignores strange dogs and other hunters. I've seen her bowl over another dog because it was in her way. This is the level I would personally expect for any hunting dog, pit or otherwise. Anything less and I would not commit my limited resources and time (a huge portion of my money is going into saving for extending the upcoming season which I would not commit to if I didn't have my setter - normal season is two months which I would be happy with.)