You know I think people underestimate Caesar's Legion a bit.
Most people think they don't use guns but the actual quote says they don't want to over-rely on guns which is a testament to how important their melee and unarmed training is.
It is true that they don't outfit their recruits with guns but that's because they're apparently designated to be cannon fodder and are usually indoctrinated slaves or tribals.
And if the captured Centurion is anything to say apparently they can kill several times their own in NCR with just melee (I doubt Centurions would make a habit of lying because lying to Caesar would get you killed and you can get that rank by getting high amounts of kills)
The problem relies in that the Legions tactics are not sustainable for long term campaigns and rely heavily on captured slaves to replenish their numbers, so High losses to Kills followed by no Slaves to capture would substantially limit their ability to project power. (Not including their over reliance on trading for firearms since they have no industry to produce their own, or their primary means of travel being on foot and the restrictions to medicine and useless armor)
Their primary strengths believe it or not is their indoctrination and ability to promote fear, with their indoctrination it allows the ability for long term infiltration and sabotage which could allow other wise disastrous campaigns into clean victories and we know their indoctrination is so good that they're willing to throw themselves on mines to clear a path (So suicidal level devotion) but it has its limits (Ex-Caesar Legion members and Terrifying Presence shows us this)
Then we get to the fear which is best shown in the case of Nipton, the citizens of the town outnumbered them and could have easily taken them out had they choose to fight back. Their crucifixion motto gives them a reputation that causes the poorly disciplined to surrender or run away making small skirmishes uncommon.
This of course is not too effective against a peer power or well disciplined force. Their 3rd greatest strength would be their numbers since they force conscription on their own population and that of captured enemies they can reasonably replenish their numbers over time.
By my estimates they would outnumber the NCR (At least 2:1) and based on quotes from the Brotherhood and NCR during the Battle of Helios.
Brotherhood numbers should be between 40 (There is at least 28 beds in the Bunkers) to 80.
Brotherhood numbers stated that there is now 5x the troops in the Mojave than there was when they fought.
Brotherhood said there was more NCR than they had ammo.
NCR forces outnumbered Brotherhood 15:1 or 20:1
Minimum is 600 Helios and 3,000 by Second Battle for Hoover Dam
Maximum is 1,600 Helios and 8,000 by Second Battle for Hoover Dam.
These numbers seem to be a fair amount considering they can eat 1,000 losses a year but still maintain a presence strong enough no faction could immediately overrun them.
Now not every NCR Soldier would be at the dam but the bulk or majority should be considering how everyone is complaining about resources and "real" fighting forces are being directed there.
So let's say 60% of the NCR was there. That's putting 1,800 to 4,800 forces there with the rest spread out across New Vegas in their outposts and garrisons.
In turn Caesar's Mojave force by scaling should be between 3,600 to 9,600. Respectable sizes I think.
