I don't think it would be China v. The Philippines due to the sole fact; China.
The Philippines(Not trying to sound offensive) really has no threat in the Armed Forces race. I mean if China really wanted to go in take over they could. HOWEVER, Amerika!
Yes good 'ole America would be like 'Da Faq you doing China?'
This goes for ANY country. If any free country is taken over by an outside force America will hop on over to check what the fuck is up. Why? Cause we're nosy assholes who think we run the world.
Conclusion; If WWIII was to break out, I'm going to say America would be involved.