Haye TKO but I think it'll go a few rounds. First Couser fight aside, Barrett is usually pretty tough.
If Couser was able to stop him early it is a near certainty that Haye will be able to do the same thing to Barrett.
Im going with Haye to get him out of there quickly. He may have to take a couple himself though. Haye KO 2.
Haye should win by ko. I'm not too confident due to the lack of fights at heavyweight for Haye. But I think he will have enough to stop Barrettt around the 7th or 8th rounds. But he might have a few shaky moments of his own.