Spoilers ahead. For me it was the Yes Man. I sided with him since I found the character funny and he was the only option I trusted. He was a robot designed as an assistant, so what could go wrong?
I went with the NCR for my first playthrough and then I joined with Yes Man since I wanted to liberate New Vegas and not have my character take orders from anyone.
Yes Man one playthrough and then the NCR on another, I think the Legion maybe once as well I am not sure.
Yes Man for me. But it was basically ME that did all the work. In these kind of games I hate being the underdog since I have all the freedom to do what I want.
Legion did on my first playthrough but on my second NCR were the winners. Never got to experience Yes Man winning the battle, although I didn't try too much to make it happen.
I went NCR and would totally do so again. But as to who really won the battle, then the answer has to be, the Courier, as he one shotted Lanius in a totally anticlimactic battle, when they first met each other. It might have had to do with the fact that my character was max level and totally OP at that stage of the game.
I was always hesitant to side with yes man. I kept getting really odd feelings about him. The NCR won the battle the first time for me. Second time I went with the Legion.
NCR remembered me too much of the things wrong with the U.S, while Mr.House was an authoritarian, and I give the middle finger to anyone who claims to be a "Benevolent dictator". I also said no to Caesar because he is completely out of his mind. That leaves me with the happy robot. Don't get me wrong, he really creeps me out, but It was the only choice that seemed to not be a moral failure to me.
The first time I played, I went with the NCR. Second time I played, I found the NCR too corrupt and went with the Yes Man though sometimes I get the feeling the robot's waiting to take over. I'm on my third run now and I'm thinking about joining Caesar's Legion to see how his faction would treat my Courier as a female.
On my game, NCR won the first time and then Yes Man won the other two or three times. I didn't like NCR that much so I decided to shake things up and went with the positive-sounding side.
