In the Japanese version of "Godzilla Raids Again", it is explained that Angilas, "a peaceful carnivore", hates Godzilla because he's a violent war-mongering monster. Since by this point Godzilla is a straight-up superhero, Angilas would have no problem with him.
The highlight for this has to be when Anguirus catches sight of Godzilla taking heavy fire from a high powered laser. One strong enough to knock the King of the Monsters off his feet and leave him in danger of serious injury or even death after repeated followup shots. Gigan and King Ghidorah stand 'guard', practically daring Anguirus to do something about it. Challenge fucking accepted seems to be running through Anguirus' mind, as he charges, utterly headless of any possible danger to himself, headlong at the tri-winged cyborg, getting a BUZZ SAW to the face for his efforts. Anguirus is heavily cut up, but keeps doing his level best to come to Godzilla's aid. Considering how the two started their acquaintance more than a decade earlier, it shows just how far the two have come. Godzilla returns the favor as best he can during the film as well, showing that the friendship is very much a two way street, and given that Anguirus has no real powers, it also goes to show how much Godzilla respects his spiky counterpart in this film, as the two are very much on the same page throughout the film, covering each other's backs as best they can the whole way through.