Seeing as this forum is packed full of military, ex-military, and experts on military, it seemed a good place to ask.
First, before going crazy about the population difference, I'm just asking about a small-scale war (if there is really such a thing), such as if China and the US were to tangle over Taiwan. Obviously if it went all-out the earth would quickly get a tad bit radioactive, so just consider a strictly confined area conflict over some territory.