here has to be times when Godzilla is embarrassed by his dorky friends in the same way Fonzi must have cringed when hanging out at Al's with Ralph and Potsy. But the world isn't big enough for both of them. One of them has to go. And true, it's usually Ghidrah.
But Godzilla has to call in allies every time they fight. He's never defeated Ghidrah all by himself.

"Destroy All Monsters" features Rodan, Mothra, Baragon, Godzilla, and Godzilla's geeky son stomping the crap out of Ghidrah for something like 20 minutes. They always kill him in the end, but if it were just one-on-one, without Godzilla and one or two of his buddies doing the tag-team thing, the outcome of the battle wouldn't be so certain. Godzilla's one resourceful monster, but he's hampered by the fact that, by the time Ghidrah starts to feature in these movies, he's essentially a good guy.

He's a friend to children, with probably some semblance of morals and ethics. Ghidrah has no qualms. He also has three heads. Almost unique among Godzilla's enemies, Ghidrah always bounces back. Who remembers the Smog Monster? Gigan? Megalon? The Sea Monster? Once they were down, they stayed down. And Mecha-Godzilla? He's just a robot. King Ghidrah has nine lives for each head. Add to his talents that he can apparently breath in the airless environment of Planet X and makes a sound like a gymnasium full of giggling lunatics and you've got one bad monster. Compared to Ghidrah, the Terminator is about as menacing as C3PO.