While this storyline is one of the most iconic in Marvel Comics history, the Ultimate Universe did something of a retelling, showing a much more brutal initial showdown between Wolverine and the Hulk. In that and the subsequent issue, Wolverine was tasked with finding and neutralizing the Hulk, as the Hulk was simply too dangerous to be left unchecked.
This is something that’s linked all the way back to Wolverine’s origin in Marvel Comics, since he made his first appearance in Incredible Hulk #181.
Throughout his Marvel Comics history, in both Earth-6, the one person who could always hurt Wolverine the most in battle was the Hulk.