You're making a mistake I see from beginners quite frequently in digital logic: assuming that there is a "default" logic level. That is, if one of them is outputting 1 and the other 0, 1 will "win" because there's something special about a 1. Similarly, I often see people assume that disconnected inputs are zero (also not true).
It's equally possible that the one outputting 0 will win. Another likelihood is that it'll sit somewhere in between, giving an invalid logic level to the next stage and risking damage with excessive power consumption (as the one outputting a 1 tries to pull the 0 upwards, and the one outputting a 0 tries to pull the 1 downwards).