I think WoG once said that Mecha-G would've stomped a healthy Kong, but I can't find it.
That said, Serious Godzilla also stomped Kong, so that's irrelevant.
As for who wins...this is a tough one, but even though I'm a Mecha-G fan, I sadly have to give this to Godzilla.
He may only be slightly stronger, but that'll likely be enough since all of Mecha's weapons besides the proton scream and the tail drill won't even scratch the Big G, and the Big G is just as clever and resourceful.
He may not kill Mecha G with one Atomic Beam, but a few of them should do the trick after a long and hard fight.