The Romans had several advantages, including standardization. Every Roman soldier could expect to be armed and armored to the same standard as any other (barring barbarian auxiliaries, the equivalent of the monster-people), and that standard was fairly high as far as line infantry went, even by high medieval standards. They were also generally better trained than your average medieval footman or crossbowman. You don't really see this same level of standardization, high minimum quality, and training emerge until around the Thirty Years War, when states were sufficiently centralized to support standing armies (as opposed to peasant levies and individual lords' little bands of men loyal to them, and to the crown through the rather highly decentralized feudal model of loyalty).
Certainly, a medieval knight would have better armor, arms, and possibly training than the average Roman legionary. But legionaries as a whole were vastly better equipped, trained, and disciplined than the average peasant soldier, and that's what counts in a large field battle. It would be rare for an ordinary medieval footsoldier to have much in the way of metal armor, usually nothing beyond leather armor with discs or plates of metal sewn in, if that--many made do with leather and thick cloth. Likewise, ordinary footsoldiers by and large didn't have much training and were armed with whatever they could lay their hands on, not high-quality blades from a good smithy.
If you could field a force of High Medieval men-at-arms equal to Roman numbers, they'd have a material advantage. But such a force would be highly difficult to assemble--you're talking about basically three classes of men: knights/nobles, the personal armsmen of the same, and professional mercenaries. A single Roman legion from most of their history was ~5,000 men, all professional soldiers, though at the twilight of the empire numbers dipped as low as ~1,000 men per legion. The number of active legions varied over history from 50+ to 28. So we're talking ~250,000 professional fighting men during the brightest years of Rome.
Obviously, you wouldn't see the total of Rome's forces drawn together for a single campaign or battle. However! We know that (probably) five legions were involved in the capture of Britain, or ~25,000 professional soldiers. By way of contrast, most modern historians estimate the size of the Norman invasion force under William to have been ~7,000-10,000 men, of whom only ~1,000-3,000 were cavalry, or roughly equivalent to men-at-arms in terms of quality of equipment and armor. I'd offer more comparisons of individual battles, but not much quantitative data is readily available about Roman troop numbers.
However, take those two forces again. Assume you've got an equal number of legionaries and high medieval men-at-arms. Again, this unrealistic force composition for the medieval side means that they've
maybe got the material advantage, which they wouldn't if the composition was period-accurate. It also means that they have no archers and are mostly composed of cavalry.
Here's a more useful wiki link. That force of legionaries will have standardized equipment to fill a number of roles, standardized use of the same, standardized tactics, unified leadership, diverse force composition, &c. -- even if the legionaries are randomly taken from every legion in the empire, they will know how to work together efficiently and effectively. The medieval force is divided--you've got hundreds of different loyalties to individual lords, knights, and mercenary captains. The soldiers on that side are at best accustomed to working with their own little bands; if they're randomly taken from fiefdoms and mercenary bands you have a largely leaderless rabble, barring whoever emerges as leaders on the spot.
So yes, if I was a betting man, I would put my money on a Roman force against even a High Medieval force of roughly equal numbers, never mind Low Medieval. I'd give better odds to a Medieval force with a realistic (and more poorly equipped) force composition solely because it means that they'd have archers in meaningful numbers.
