The american film had King-Kong winning, the Japanese film did not have Godzilla winning.
In the american film the movie ends, but at the end of the japanese film, you hear Godzilla roar one last time and it blacks out.
Those are the only differences.
And as for now adays, if you have seen Final Wars, you would know King Kong is destroyed.
Godzilla vs. King kong is a difficult one because of the circomstances. For example what generation of Godzilla? The movie involved a fight between King Kong and the Showa Godzilla but had King Kong had a scrap with the Heisei Godzilla the chances of him winning would have been greatly reduced. The 2000's series Godzilla would have stood a better chance of defeating King Kong to. All three Godzilla's have different powers and sizes. So it depends on the Godzilla in question.