Strictly speaking there are a lot of analogies here. Warhammer is a giant rip off, errr, homage, to Michael Moorcock's "Champion Eternal" cycle (which includes more than just Elric) right down to the taint of chaos, and how a lot of the units happen to look. Moorcock was himself inspired by HP Lovecraft and other, similar writers. Some of his earliest work like "Sojan The Swordsman" was created due to him not caring for some of the limitations placed on the mythologies of other writers who allowed their characters to be borrowed. All told it was a pretty incestuous period of writing, even involving a bit of necrophilia in using the work and being directly inspired/ripping off people who were dead. Copyright laws and such weren't quite what they are now, and the community actually encouraged this to an extent with a lot of odd crossovers and things being borrowed sometimes just occuring based on an exchanged letter or handshake.
The point here being that both universes have a lot of overlap in their concepts.
Overall, I'd give this one to Lovecraft's mythology. Cthulhu himself is actually a pussy, he's just the high priest of the old ones from a race that happened to colonize earth during the extensive pre-history. Cthulhu not only got stunned by a boat, but his entire race was defeated by the Yithians, who were themselves driven off earth by the Flying Polyps.
On the other hand when you start getting into some of the concepts, and don't argue the idea that they are all the same beings under differant names, in differant worlds (which could happen), the bottom line is that the forces of Chaos in Warhammer get spanked regularly, including the chaos gods when they run into other god-class opposition. Heck, Sigmar did a bit of a job on them, and he was a mortal at one point. In Lovecraft's mythology part of the terror is that there are no benevolent powers that can stand against them, these things are pretty much the actual truth of the universe, that's why it's cosmic horror. Deities like Hastur basically ARE the center of the universe... and well, the chaos gods might be powerful entities, but if they both existed they wouldn't hold a candle to that.
In the spirit of things an actual Lovecraft/Warhammer crossover might be an unheard of situation with say Chaos and the rest of the world actually working together to protect reality (which can't be corrupted and conquered if something else takes it all over, or worse yet... eats it), you know where the Dwarf gods or Sigmar (via Sigmarite visions) actually tell their minions to coordinate with their enemies, as there is now something worse than the encroaching chaos wastes.
Such an alliance couldn't KILL the ultimate enemies, but could perhaps imprison them, lock them out of the dimension (for a time... only for a time), and defeat the minions trying to give them full access to the world.