Mjolnir is a weapon that smashes bones. The Hulk's healing factor is fast enough that that does not bother him much. We have never seen Thor get a clear shot on the Hulk's head. The writers tend to always have something interrupt. So if Thor did split the Hulk's head open we don't know what would happen.
An ax is different. If granted a free shot than Thor or Hulk could quite easily take off the head of the other. Hulk actually is a bit worse. He usually has no real way to block weapons that can cut him. If it only gets off half of an arm he can heal. If it cuts off an entire limb he is screwed. Thor at least has been shown blocking axes with Mjolnir.
There was a story where the Hulk's nose was bleeding, but Thor got the worst of that fight. I think it was a Stan Lee/Jim Shooter story in Thor's book in the 80's. I thought the Hulk was out of character in the story and that the art was attempting a more brutal version of a Thor/Hulk fight than we're used to seeing.