I would choose "win the war" simply because we already know the outcome of that decision, and that decision is much better than the other. The greatest good is the lesser of the two evils.
Another problem is that choosing to "win the war" will make the leader look worse if his options were ever discovered. Emotionally, choosing to win the war would be much worse because your own citizens, your own countrymen die. Strategically, choosing to protect the city would prove to be much more traumatic for, not you as the leader, but the country as a whole or the 10 million that die.
Analysis over, sorry for putting you through that.