So let's say the union of both chains is the rule. The problem becomes how many chains do we allow in the union because it is unbounded. If we place a bound on it, the adversary can Sybil attack the bound.
It has to remain unbounded for it to have any chance of working. In this case, such an attack would bring consensus to a standstill - but would this be a sustainable attack? If you imagine the attacker generating new POW transactions continually to create the bigger union, this is going to get quite expensive for him quite quickly... whereas the minority do not need to expend as much energy, since they are just bundling transactions not fabricating them.