I mean, this isn't really a question you can answer objectively because there isn't really much in the way of direct data. Personally I suspect that the Roman army would not have much trouble, given that it was a true, professional fighting force with complex logistics and supply lines, a dedicated officer corpse, high coordination between different forces, enormous divisional spirit, dedicated engineer corps, etc. This isn't to say none of these existed in the middle ages, and certainly Medieval armies were made up of people who spent all their time fighting and they definitely possessed much more organization than is the stereotype, but not the sort of organization the Roman empire managed. Simply put, none of the Medieval polities had the resources capable of doing so. (dinging /u/MI13 to keep me honest)

A lot of times (even n this subreddit!), incidentally, these sorts of discussions devolve into a sort of wrangling over technology and comparing sword types and the like, which is completely the wrong way to look at this. If you are comparing, say, the armies of WWII then sure, look at tank armor thickness. But ultimately a sword is a sword, and while some swords are better than others it isn't as though any one contains a decisive technical edge over another.