Option 1 - Predators Win
If the Predators defeat the Aliens, then their 'rite of passage' will be complete, and they will leave, returning in another hundred years or so - next time probably without killing any humans during the ceremony, since there's no reason to believe that humans would coincidentally be in Antarctica again that time.
Also, depending on global warming, Predators will probably swing by every couple of years and kill a few people in a jungle/desert, but they were going to do that no matter what happened in Antarctica.
Option 2 - Aliens Win
Upon killing the Predators, the Aliens would then freeze/starve to death in the Antarctic.
Either way, I can't really see how either one of those results can be described as 'We Lose', assuming the 'we' there refers to humanity.