Shat is only like 5'10" (advertised, I think he may be shorter than that in reality) and in his prime, was about 175 LB. Brooks is 6' 1" and in his prime was about 200 LB. Based on that, I would say Brooks has better reach and is stronger. In real world, Brooks would take Shat, but since we are talking characters...
Kirk has his Kirk Fu and as soon as the shirt rips, it's all over.
Sisko may have decked Q, but Kirk bitch slapped Trelane (who could have made Kirk just as dead just as fast as Q could have with Sisko), Karate chopped Gary Mitchell (same as Trelane), laughed in the face of Apollo, pnwed Khan in a fist fight, laid some smackdown on Captain Ronald Tracy, kicked lord Kruge off a cliff, and held his own with Spock, and a boulder-hurling Lizard man!