Something I've considered- set in a fictional world where two cultures clash- one whose military is styled after the legions of Ancient Rome fighting against an army based on England or France in the Middle ages, (bowmen and infantry led by knights with lances). Assuming they had comparable numbers, who would likely be at a disadvantage technologically speaking?
Military professionals know that it is a rare instance where technology alone decides the issue on the battlefield. Even today, we see the high tech military forces of the West being fought by insurgents armed with infantry small arms, improvised explosive devices and communicating over the cell phone network. Roman weapons like the the glades and armour (either chainmail or later Lorica segmental wasn't fundamentally different from weapons and armour of the Medieval period.
The primary difference between the Legions and a Medieval army isn't really in technology, but rather organization, strategy and tactics. The classical Roman legions were a heavy infantry force with a small component of cavalry and ranged weapons like archers, supported by professional engineers and access to heavy weapons ranging from scorpions to catapults of various sizes.
The Roman Legion was also supported by an efficient system of roads and logistics stretching across the Res Publica and later Imperium, not to mention ships and naval support.
A Medieval army was organized differently. Without the massive bureaucracy and logistical organization that characterized the Legions, a Medieval army would have great difficulty taking to the field for extended campaigns. Being forced to "live off the land" made the general shape of a campaign into a giant raid (known as a Chevauchée), whose main purpose was to despoil the countryside and deprive the agricultural produce and other wealth to the "owning" side. The Knights and Men at Arms were not professional soldiers the way the Milites and leaders of the Roman Legions were, but were still skilled and fearsome fighters with a lifetime of very specialized military training behind them. Mercenary soldiers and "Yeomen" could be quite deadly as well (English and Welsh longbowmen were particularly good examples of this).
Yeoman Archers are hired for their skills
Tactically, the Medieval army could probably move faster given the larger percentage of mounted men and the coverage the much larger proportion of archers could provide, while the Romans would be able to use defensive tactics to stand their ground and the flexibility of their Manipular formations to react to movements by a Medieval army, trusting i their ability to absorb the shock of contact and then grind the enemy down with their deliberate advance. If the battle took place in Roman times, the Romans could use their logistical advantage to sustain themselves, while depriving the Medieval army of supplies (they would have to get them from fortified Roman cities and military camps), while if a Roman Legion was operating in Medieval times, they would be the ones cut off from supplies and support.
A Legion drawn up in formation. In battle, the maniples and centuries could rapidly move around the battlefield rather than fight as a single, solid mass
So the real answer is the Romans have an advantage due to organization and technologies such as engineering to build roads, erect fortified camps and move and store supplies.
Rome really had two great weaknesses in campaigning:
Firstly, they weren't too successful against Cavalry. This was most evident at Carrhae when the Parthian horse archers slaughtered a good chunk of the legions, while the heavy Cataphract charge finished them off. Also at Cannae, where Hannibal's cavalry chased off their own horsemen, and wheeled around to slaughter 30,000 foot legionaries in a single day. Medieval Knights were some of the best heavy cavalry in the world, so this would be a major advantage for the Medieval side. They also maintained some cavalry archers, though the Muslim armies of the era (and later the Mongols), were much more reliant on them.
One example Battle you may want to read about is the Battle of Manzikert, in which Turkish horse archers defeated the Byzantine army. True, the medieval Byzantine army wasn't exactly like the Roman Legions, but I believe it was somewhat similar, and it's lack of mobility made it vulnerable and gave the mounted enemy the initiative.
The Roman's other great military weakness was their inability to deal with asymmetric warfare and ambushes. This was most evident in their great military defeat at the Teutoburg Wald, where a Germanic force ambushed and destroyed several legions. Medieval armies weren't all that fond of these tactics, but their reliance on excellent archers and cavalry would have likely given them the option to pursue this path.
Finally, the Longbow was a critical invention which allowed the British to win several great battles against the French in the 100 Years War (notably Agincourt). A large, slow-moving Roman Legion would have been sitting ducks if faced by massed Longbow fire, and would likely have collapsed (the Tortis formation, where they locked their shields, gave some protection, but the slaughter at Carrhae shows it wasn't nearly enough.
Ultimately, the Romans would almost certainly win a hand-to-hand, face-to-face fight, but Medieval warfare no longer revolved around that, and the heavy Knights and Longbowmen would likely make short work of the Legions before they could close for battle.
Still, it would have been fascinating to see. The Roman's best bet would have been to: 1) Recruit Longbows as auxiliaries. 2) Develop a shield that can block a bodkin arrow. 3) Fight on the defensive, making use of stakes and earthworks to blunt enemy Cavalry charges.
With these conditions met, the Romans would likely prevail.
Depends on when in the Middle ages you're talking about, and when in the Roman period you're talking about.
Because Ancient Rome lasted for quite awhile and there were advances in armour and fighting techniques.
Same too for the Middle Ages, it lasted for quite a while, and there were advances during the time period as far as warfare and metals were concerned, especially when it came to the longbow, which wasn't in wide use for most of it.
But, I am going to assume that this clash is going to be Rome at the height of tech vs. Middle Ages at the height of tech.
Most Roman legions used chain mail, which is NO defense against the longbow, used at the height of Medieval warfare. Yes, they did have some troops that used segmented armor, but the design was not great against arrows. If you look at the armour used in the Middle Ages, you'll see that the best stuff is curved, but Roman armour wasn't designed that way.
The shields of Romans were mostly made of wood, and surprisingly, would be somewhat effective, up to a point, in at least catching arrows.
In both the Roman army and Medieval armies, most troops did not have full armor.
Now, Romans have always excelled is in discipline and tactics, whereas the discipline in Medieval armies could sometimes be a bit rag-tag. Armies were outfitted in Medieval times at personal expense of Lords or of the men under them, to fight under the King for a cause. But Romans were more centralized and uniform when it came to equipment, training, and their supply chain.
Cavalry is going to be a strength on the Medieval side--because Romans were never well-known for horsed combat, though at the height of the Roman empire, they DID have mounted cavalry, and it was pretty good for its day, they may be outclassed by knights, just because there's a little more emphasis on horsed training.
But, surprisingly, Romans did have lances, and they were comparable in length to the ones used by Medieval knights. The Roman horses were also outfitted in armor, just as the Medieval ones were.
A seasoned group of Crusaders would be an equal match for a comparable group of Legionnaires.
Then, we come to the development of artillery in the 1300s! It was this advance, besides the longbow, that changed warfare and tactics forever. This is going to make things very difficult for your Romans.
So who has the advantage? I believe this would actually be close thing because they have advantages in different areas, but I am going to have to give it to the Medieval army!