We'll assume Caesar's Legion and Caesar's Legions are equally numbered. By the time of Fallout New Vegas, the NCR is a large and developed nation state with industry, economy, and society. It's military utilizes vehicles and maintains a corps of troops armed with power armor. Caesar's Legion would require tens of thousands of men to threaten them, which is probably the case according to in-game lore.
Julius Caesar is an excellent strategist and tactician. He is classically trained and has fought and won in multiple wars. His primary attribute, however, is not in military acumen but in political mastery. He seized power over the entire Republic from a cabal of powerful enemies united against him while winning the favor of the common people. His ultimate military victory over the forces of the senate was a matter of luck after Pompey had outmaneuvered and trapped him.
Edward Sallow is brilliant and highly educated. While perhaps not as naturally politically gifted as Julius Caesar, he has the advantage of having studied all of Caesar's, and indeed all of Rome's, history, strategy, and mistakes. Because of this, retrofuture Edward Sallow is the superior military tactician.
Caesar's Legion is primarily armed with hockey pads and makeshift post-Apocalyptic weapons. Their men are trained in discipline, but through an equally makeshift regimen developed only recently by an academic who studied organized melee combat in books. Their primary opponents thus far have been tribes of post-Apocalyptic survivors equally ignorant in the ways of combat and the art of war. Their one advantage, as has been mentioned in other posts, is firearms. But just as everyone else has detailed, they are distributed sparingly, and only about one in ten of Caesar's Legion carry one.
Julius Caesar's Marian Roman Legions carry specially designed weapons and armor perfected over the course of hundreds of years of warfare and crafted specifically for melee combat by engineers and blacksmiths throughout the Republic. Their training matches the quality of their equipment, developing men into hardened soldiers through time-tested methods under the tutelage of master warriors with decades of combat experience. Caesar's men in particular, at the peak of his military campaigns, would mostly be battle-hardened veterans. All of these advantages are, of course, out the window once they start catching bullets.
In any situation in which a pitched battle would occur between Edward Sallow and Julius Caesar, Sallow would undoubtedly win. Sallow knows everything about Caesar. He developed an entire persona based on this knowledge. He knows how Caesar will move, how he will react, and how he will think. His one disadvantage is the quality of his troops. He knows Caesar's veteran legionnaires will know nothing but the exact type of antiquated warfare his futuristic tribal conscripts are now forced to fight. The Romans would slaughter his men in their football pads in face-to-face melee combat. So Sallow would funnel the Romans into a trap, would goad them into attacking a seemingly weak, outnumbered, or highly exposed position. And he very well can afford to be highly exposed, outnumbered, and in a comparatively weaker position all simultaneously, because even with a limited distribution he still has thousands of troops with modern rifles. A .308 round from a hunting rifle will slice through the steel plates of Lorica Segmentata armor like butter. Even .22LR will penetrate the armor at close range. It would only take a few minutes of concentrated accurate rifle fire to completely obliterate any Roman foot or horse charge, from far outside the range of any Roman artillery.
Caesar's only hope for victory would be to somehow learn of the technological marvel of modern firearms and adapt accordingly by avoiding any direct frontal confrontation with Sallow's forces. His best bet would be to ambush Sallow's forces, say in dense vegetation or in the ruins of a post-Apocalyptic urban area, and close into a melee fast enough to prevent Sallow's riflemen from organizing. The legionnaires could then maximize the advantage of their superior melee abilities and equipment and kill Sallow's men at close range.