I'm glad the NCR won, despite the close battle. The Elite warriors of the Legion need more firepower to pose a serious threat to the whole of California. For now they only pose a threat to the small area surrounding The Hoover Dam. The NCR at their best is devastating, because they include a mechanized and air force within their ranks. The Legion just don't have the equipment to bring down machines like that. Who knows, perhaps in time they will acquire a greater force.
The securitrons of House would also be quite a battle, but I do believe the NCR could prevail. Human's are more tactically agile, and the securitrons are usually controlled by one high commander. And I never understood how they could repair themselves in real life... Unless it was a very minor damage.
The Brotherhood, even with their skillful soldiers would fall to the NCR. Although if they would start to recruit from the outside, set up a stable government, start a succesful economy, and show to me they can lead then they might gain my support.
Overall such a massive military as the NCR is not to be reckoned with. They may have mediocre leadership and a lack of skillful troopers, but they do have rangers and the skill they bring to the table. Caesar has a powerful force, but it is not meant to bring down the NCR. It is meant to take down opposing tribes, who do not have an air force or masses of armed soldiers.