Is this really knowable at this point? It looked to me like Kong was the good guy (Godzilla was attacking Japan and Kong was brought there) and the characters were clearly rooting for him (Kong). The ending appears to me that Kong vanquished Godzilla (the objective achieved) so, by getting the job done and going home Kong seems to be successful, therefore he's the winner.
But don't pay any attention to me; I think it's clear that there are different endings to the original Japanese KKvG and the American adaptation (it's ipso facto) and Godzilla's gender has always been unknowable (which is Toho's consistent doctrine). This puts me at odds with almost everybody, so sue me.