Shaggy Man can't die or be knocked out. It's impossible. The JLA had to teleport the bastard to the asteroid belt in order to "beat" him. The combined assault of the entire JLA and the Ultramarines proved fruitless.
Shaggy Man is initially stronger than Savage Hulk. However after a while Savage Hulk would reach his level. This battle would go on forever. Draw.
Draw. Shaggy is initially quite a bit stronger than even Superman, so Hulk would take a while to get there. He would, eventually, but Shaggy is every bit as impossible to kill as Hulk...maybe harder.
And that's only Doomsday that can't be beaten the same way twice...not sure where you read that Mider, but I don't think the same holds true for Shaggy.