Since both constantly emit radiations, by absorbing them, they would both gradually become stronger as the fight progresses, but not much would change.
IDW Godzilla has not only AP but also a slight range advantage with the Atomic Breath. Plus, he tends to use it much more in character.
Monsterverse Godzilla, however, is tremendously older, and thus much more experience, and has also a Lifting Strength advantage (and yes, despite the Ap disadvantage, MV Goji is much more of a physical fighter than his IDW counterpart), a speed advantage and he' also slightly bigger, which may be either a good or a bad thing for him depending on the situation.
They surprisingly even things out. I guess I'll go inconclusive since it could go either way.
I know this is added but I hope you don't mind me giving my two cents.
So Fire Godzilla was able to three shot an amped King Ghidorah, who scales to if not may be the asteroid from which the teraton feat comes from. Given the one shotting page says it requires a 7.5x gap, a 2.5x amp per attack should be reasonable (possibly slightly less since the middle head survived but you can argue that's due to Ghidorah's mid level regen). Thus we can easily scale him to be worth 9 teratons. Or...we could scale him to the KT event.
IDW Godzilla is far stronger than the 4.78 teraton feat by Rulers of Earth however, seeing how with his full power he could one-shot a SpaceGodzilla trilopod who was superior to the actual SpaceGodzilla, who bullied Battra very easily. With the one shotting page in mind, 35.85 teratons could be argued for full power RoE Godzilla.
Both could be argued to multi-continental as well; but that's another essay in its own right.