Quote Originally Posted by QuintusSertorius
The late "legionaries" of the 3rd/4th century AD, and those of the late 1st century BC to first century AD have little in common besides their names. Recruited from different peoples, trained differently, different equipment and so on.
Mh, obviously. Didn't think about that.

That makes the whole thing different, but I'd still bet on the knights on a direct face-off. However, as you pointed out before, there are a lot more variables other than equipment... we could just say for simplicity of our "hypothetical experiment" that they start out in the same "state"; meaning:
no-one's surprised
they have the same morale (impossible in real life I think, but this is hypothetical)
they are fully rested
they have the typical training of soldiers of their kind (some questions of the meaning of "typical" could arise here)

However, what about the terrain? We could say "A flat plain, so no-one has higher ground etc. etc."; but a flat plain is an OBVIOUS advatage for the knights, who can charge easily. If they fight in the woods, horses are almost useless, and the legionaries would have the upper hand. If they fight anywhere, the terrain would be more suited to one or the other...

You were right, I don't see any easy way out of this...