Godzilla and Pacific Rim would actually make sense. The alien Kaiju are attacking Earth, they are destroying it and destroying balance. Godzilla rises to defeat the Kaiju, but the foolish humans thing that he is one of them and sends Jeagers to kill him. Godzilla beats them up badly, until our main human lead (who is a Jeager pilot) realizes that Godzilla is actually trying to help them, but the humam leading factions dismiss him as a "Rogue Kaiju". Stuff continues to happen until humans finally realize that Godzilla is helping them (He acutally never started a fight with the Jeagers, they always attack him while he is on his way to beat up the next Kaiju). The Jeagers and Godzilla fight the Kaiju who summon their big bad category 6 Exterminator and and the cat-6 turns out to be almost as strong the big G. Godzilla evantually rips the Kaiju's heart off with his bare claws (plus a tiny weeny bit of help from the Jeagers, who are busy fighting the smaller Kaijus). Godzilla enters the rift, goes to the alien demension, and goes through some classic city-destroying when he decimates the alien world's cities.