I wasn't really rooting for either them. I wanted Blue team is work out what was going on, and in the end I wanted Osiris to catch up to lend a helping hand. There was no real conflict apart from the old man fight between Chief and Locke.
I didn't find a great divide between the two teams as it all seemed to be lack of communication that caused the situation. That is especially true after the face-off between Masterchief and Locke relatively early in the game. Before that I was rooting for Blue Team to find Cortana and "figure what the hell is going on".