Godzilla probably takes it, but by no means a stomp. Just hear me out. First, there's the amount of abilities Godzilla has at his disposal. Bigger size, omnidirectional pulse, and more makes this a win in his favor, despite being a huge jobber. Second, his Regenerationn is a huge factor. If the Golem tries to kill him, he can just regenerate, considering he regenerated without any molecules.
Sure, there's the whole "i can make my head intangible" ordeal, but then there's the size difference. Big G can either blast down the body once the head comes off, step on it, or just brute force it. Either way, once he destroys the body, the Golem is done for.
Overall, Godzilla is stronger, more durable, far bigger, way more abilities, and can easily break the Golem down. The Golem may have his intangible head, but Godzilla can just use Atomic Breath on his headless body, and it's all over.
Winner: Godzilla