A late roman comitanteses Legion (1500 legionnaries) would easily defeat the same amount of soldiers of a medieval army.

To understand why we have to understand how the Late Roman army fought :
Weapons :
Defense : late roman legionnaries used round oval / lenticular shield (scutum), a ridge helmet that covered, mail shirts (lorica hamata) that covered the arms and thighs and for some military units scale armors (lorica squamata) particularly usefull against arrows.
Offense: the primary weapon was a 2 to 3 meters spear (hasta) and for close range fighting a spatha (a sword longer than the gladius)
Tactics : Beggining in the 3rd/4rd century AD, the method of fighting was, what Sylvain Janniard calls the para-phalanx, similar to the Macedonian phalanx, soldier shields to shield and spears to the front, and the front soldiers wearing leg protection advancing in disciplined steps against the enemy.
With this formation repeated on several ranks, at the back of the formation soldiers and archers could throw several projectiles : plumbatas (lead darts), arrows (shot from bows or manubalistas) and small javelines.

We could well imagine that this type of compact formation with the roman discipline faced against unevenly armored medieval soldiers as well as light cavalry could prevail.

As for the cavalry, the difference with the cavalry/chivarly of the medieval period is that the spurs weren't invented and used yet (it became common after 600 for the "Byzantine" soldiers) so that the roman army cavalry had less shock while using a spear but still used it (as well as javelines, plumbatas and bows) to fight against cavalry and infantry.
Cavarly archers were widely used by the Romans and its allies, inspired by the Huns : https://www.academia.edu/41222919/Procope_les_Huns_et_les_transformations_tactiques_de_la_cavalerie_romaine_au_VIe_si%C3%A8cle .
Heavy armored cavalry, called cataphracts, existed also but used scale armours instead of the medieval plate armours.

Let's also not forget that the Eastern Roman Empire (Called Byzantium by the historian Hieronymus Wolf only in 1555 ) existed till the fall of Constantinople in 1453 and used the same tactics as the late Western roman empires against.

The more dangerous medieval weapon for a late roman would be heavy crossbows but a para-phalanx formation would protect roman soldiers advancing on the battlefield.

It is always hard to imagine battles between soldiers from differents eras but as for medieval and roman era soldiers, technology (spurs notwithstanding) didn't evolve much, until the massive use of powder weapons.

Sources from the Late Roman Empire:
Epitoma rei militaris by Vegetius, Res Gestae by Ammianus Marcellinus, Zosimus' Historia Nova, Strategikon of Maurice (for the Byzantine Empire)

Modern Sources :
R. Dixon, "The Late roman army "
Articles on Academia.edu by Sylvain Janniard : https://univ-tours.academia.edu/SylvainJANNIARD in particular https://www.academia.edu/35253479/Le_maniement_des_armes_offensives_dans_linfanterie_romaine_tardive_IIIe-VIe_si%C3%A8cles_apr._J.-C._dans_LIBERA_CURIOSITAS_-_M%C3%89LANGES_DHISTOIRE_ROMAINE_ET_DANTIQUIT%C3%89_TARDIVE_OFFERTS_%C3%80_JEAN-MICHEL_CARRI%C3%89_%C3%A9d._C._Freu_S._Janniard_A._Ripoll_Brepols_2016_p._43-54
M.C. Bishop, J.C. Coulston, "Roman Military Equipment from the Punic Wars to the Fall of Rome, "
T.Völling, « Plumbata - Mattiobarbulus - Martzobarboulon? Bemerkungen zu einem Waffenfund aus Olympia », Archäologischer Anzeiger, 1991/2, p. 287-98.