A fight between Jackson and TR both in their prime would have been fierce to say the least. As tough as Jackson was, Roosevelt was a trained boxer. I still would not count Jackson out tho. He might just find a way to win.
With guns I would go with Jackson. TR loved guns and shooting but admitted he was a mediocre shot. It might have had something to do with his poor eyesight.
I forgot to add, they may well have killed each other. Neither would have given up.