Okay, I'm a HUGE fan of both these characters/monsters, but I've been seeing this match/argument idea a lot lately and honestly it kind of bothers me because it's mostly being argued by people or fanboys that have NO idea what they're talking about. Many if not MOST Godzilla fans don't really know Lovecraft and have probably never read anything about Cthulhu; AND in turn, many Lovecraft fans don't watch many Godzilla movies and consider them to be cheesy, low-brow entertainment. And it's not like either side is too wrong or right, correct statements are brought up, but with two sides that are both so bias, it's almost impossible to get an argument that's reasonable or apt in the slightest. So being a fan of both characters, I'm here to tell you why this VS match simply does not WORK... In my opinion.
Now as a huge Godzilla Series and Lovecraftian Horror fan, I have to say that this battle is pretty much irrelevant. I mean, the main issue here is that these Two Monsters/Beings come from two very different storytelling mediums.
Cthulhu arose from the Horror Stories of H.P. Lovecraft where humanity was defenseless against a force far beyond comprehension. And Cthulhu was the Ultimate representation of an enigmatic outsider that couldn't be stopped or understood by the incompetent human senses. It is something we were never meant to know of and much less witness. To fight against something like that would be silly.
Whereas Godzilla was originally a Monster representing the horrors that Nuclear War can create. He was basically a manifestation of the worst products our World could create. And in the later films he became the star of many really cheesy but fun Monster movies that would portray him as a hero, villain, or anti-hero. His characterization would alter from time to time and his powers and size would alter too depending on the generation.
Both are characters/monsters I love and really have nothing but appreciation for, but they are both VERY different. It's like having a battle between Goku and Jesus or The Thing against Scott Pilgrim, it just doesn't feel right.
Again, no disrespect, I just don't think you could make a real battle with it in my opinion,