I'll asume we're talking about the best version of Qawi as a cruiserweight circa 1985 and 1986. If Haye is able to keep the fight at a distance, he would have a clear advantage because of his height and speed of hand and foot. However, despite Haye's handspeed and accuracy, he wouldn't find Qawi an easy target like Maccarinelli or even Mormeck. Qawi had fine defensive skills and was a master at rolling with and slipping punches. Haye certainly has the power to hurt Qawi (and just about anybody for that matter), so he’d have to be cautious early when Haye is at his absolute sharpest. I think Qawi would survive any early onslaught from Haye, eventually forcing him to fight in close. Qawi was very adept at getting closer to taller fighters. We’d see him get into his usual crouch and counter in between Haye's wider punches. Haye has a leaky defense, so Qawi would find it easier to hit him flush that vice versa. He’d also invest in a good deal of body work and bully him a little bit. Haye, the less durable fighter, gets more and more tired as the fight enters the mid/late rounds. The Camden Buzzsaw grinds him down for a stoppage.
mos def qawi. main thing is stamina and pressure. haye maybe a good puncher but his stamina is in question...well actualyl it was answered by thompson but whatever. qawi was as his nickname suggests a buzzsaw he cut down everythign in front of him throwign shot after shot. while haye wouldnt be able to get out of the way of him nor be able to knokc him out (evander landed a peach of a right cross when qawi throws a left hook one in a life time shot) qawi wins...evander is one of the few cruisers i thikn could beat him. at light heavy qawi was easy to get out of the way of due to being lighter and faster but qawi at cruiser i feel is a far more scarier fighter.
At this point I feel Haye gasses, as has been mentioned, and Qawi takes him out. We saw Haye gas after just a few rounds. I think some extra pounds might help him, stamina wise.