I'm pretty sure the average Roman Legion under the average commander would lose to the average 15th Century English army.
Badly at that.
Taking into an account that in the 15th century the English lost the 100YW and had been kicked out of France, I’m afraid that your opinion about quality of their army is more than a little bit exaggerated. 😂
English armies substituted veterans with mercenaries and men-at-arms, while possessing much superior cavalry and absolutely devastating ranged combatants.
Deadliness of the archers is grossly exaggerated. Even at Crecy the French knights managed to get all the way to the the English ranks and at Agincourt the dismounted French knights managed to walk slowly through a muddy field under barrage of the archers. And it does not look like they were excessively deadly at Fromigny or Patay (in which 5,000 longbowmen had been defeated by 180 heavy
knights later reinforced by 1,300 mounted
men-at-arms
If it had been English at Cannae instead of the Carthaginians, the battle would have ended in half the time. You'd be substituting slingers with Welsh Bowman, and the cavalry on the flanks would have stirrups.
To start with, all of the above does not make a slightest sense because English armies of the 100YW never were anywhere close to the 50,000 that Hannibal had at Cannae: Poitiers - 6,000, Crecy - 15,000, Agincourt - 6,000-8,000, Patay - 5,000, Halidon Hill - 10,000. Then, an example when a winning side had a military genius as a leader (AFAIK, none of the English commanders of the 100YW ever had been seriously considered equal to Hannibal) and the losing one a complete nincompoop is not a proof of anything (army of the lions led by a sheep, etc.).How about something like Zamia?
But let’s get along with the fantastic assumption about the numbers which your claim implies. The center of the Carthaginian army was not held by the slingers and dismounted knights would not held for a long against the Roman infantry. BTW, a parallel between the slingers and English archers is not working due to the different tactics: unlike the slingers the archers had been acting in a static formation, preferably protected by some natural or artificial obstacle. The archers would not be effective against the infantry having big shields and trained to use testudo formations. So almost as soon as the Roman infantry gets close (suffering minimal damage), the English front is broken: unlike Hannibal’s infantry, the archers are not good in hand-to-hand fighting against high quality infantry.
I quite agree regarding advantages of the medieval cavalry over what the Romans had at the Cannae but not because of the stirrups (popular but phony argument) but because it was
much heavier (heavier armor and long lances and swords against the short spears and swords) and destreyers were much bigger than what the Romans had. However, ability of the knights to conduct the same maneuver as the Carthage and Numidian cavalry at Cannae is a big question mark. There is no doubt that they’d break the Roman cavalry but the knights were routinely very bad and in maintaining a discipline during a pursuit and the cases when they managed to stop a pursuit, reform and launch a new attack had been quite rare in the medieval warfare. In the best case scenarios it was taking a considerable time to rally them around the colors. So chances are that by the time they are back on a battlefield the English infantry disappears from the field.