Briggs doesn't have the speed to land on Haye though being too muscle bound now. He isn't going to be landing KO shots when he's not quick. That said I think both Klitschko's beat Haye. Haye's lack of workrate and leaving his chin open will make it easier for both brothers.
It would be a totally different fight. I think Haye would stop Briggs in about 8-10 rounds. Fact is Briggs is shot, he brings nothing to the table other than size, heart and durability. I see Haye's speed as a factor as he will be able to catch Briggs with shots he won't see coming, unlike Vitali who doesn't have the speed or power of Haye. But the fight would be at least slightly competitive as Briggs won't have as much difficulty landing shots against a smaller man like Haye. So Haye may stop him but it won't be as one sided a fight as Vitali/Briggs.
that long paw jab like fly swat was the key of keeping the cannon away. That paw is significant and may keep haye from getting inside.
One thing is clear, Haye is extremely afraid of either Klitschko and broke two contracts with them and ran. Rumors are that Haye is trying to get out of his mandatory with Chagaev and will fight Holyfield next. Audley just might knock him out first though.