Damn, a 120lb Pit bull. I didn't know they reached that weight. But yeah, I would still say the cougar would win: They're 115-220lbs. Ultimately, if you place a dog versus any type of cat of equal weight, I would say the cat will likely win. Domestic cats don't have the jaw to bite like a dog of equal weight does (even in this video), but any cat larger than a bobcat or lynx will have sharper and more precise claws in addition to comparable teeth and jaw strength.
On the other hand, a dog—pit bull in particular—may have more stamina and resistance to pain. So I don't know. Either way, I ultimately wouldn't want the fight to happen in the first place.
On a side note, my girlfriend's cat stood her ground around her two full-grown 100lb dobermans; in fact, she clawed them in the nose when the dogs cornered her. Now she rules them, haha.