That's a tough one.
If we're talking just in a physical battle, than Cthulu might have a bit of an edge. He's more humanoid, so he could easily outmatch Big G's short arms. They have about the same Intelligence.
If we're talking about any other category, Cthulu wins indefinitely. There's always something new and disgusting that that thing can do that we've never heard of. The fight could only last a few seconds if Cthulu just pulled some dark magic junk and turned Godzilla into a toaster.