Agreed that legions beat phalanxes; the Spanish reinvented something similar when they discovered that swordsmen could defeat squares of pikes and halberds. No argument that pike squares/phalanxes are the most cumbersome of infantry formations. But they do offer the best infantry defense against heavy cavalry. The Roman victories against Persian cavalry notwithstanding, I doubt they were fighting knights in mail or plate armor, armed with 10-foot lances and mounted on destriers the size of modern Percherons. The shield wall became more and more obsolescent in the face of heavy cavalry during the “Dark Ages” and had virtually vanished by Hastings. So again I ask, what a Roman general would do after seeing knights cut through his legions like butter?
What Roman generals did after the double envelopment at Canne. After the defeat at Carrhae. After the loss of Varus’s legions in the Teutoberg Wald. Adapt and counter. A standing professional army with superior organisation can always adapt to defeats. A medieval European army, raised for a campaigns can fight in only one style. After the above defeats the Romans brought in more Archers and Cavalry. They learnt close coordination.
Well, the easiest way to tackle this would be to look at the changes in the Roman army during those 1000 years and see which were beneficial and which were not.
The Romans had two technological weaknesses, metallurgy and horse breeding. They were aware of both and did their best to work around. Unless you’re a really good smith, long swords tend to shatter or bend, being either too stiff or too soft. Romans were in awe of Celtic long swords, but turned their own weakness to a strength by changing the swordfight to a clash of a really dense shield wall. This makes a long sword much less useful. This was effective in infantry melee. But the swords got better and better all the time. Later Roman armies would turn to longer swords. Probably because it had to be done in the face of better swords. Also, because infantry fighting became less important with the increased strength of cavalry.
Romans understood the importance of good cavalry. But their core areas are not good traditional breading grounds and the key factor of the time was the increased number of increasingly big horses. Their response was two-fold: recruit all nomads they could and further develop the cataphract to be so heavy that a small number matters and horsemanship doesn’t. The extent to which late byzantine empire relied on cavalry is telling. It is not just because the power was going to the feudal class: the power was going to the feudal class because the cavalry was irreplaceable.
Talking of classes, the strong suite of Caesar’s army certainly was that it represented a uniform massed army of a “nation”. Medieval armies were small, reliable elite units surrounded by local armed populace with shitty weapons and no skills. I think this is Caesar’s only chance. But I have to echo the Mongolian horde argument: steppe people are extremely organized, I guess because controlling vast numbers of sheep with some riders just takes a lot of discipline. The hordes are so innumerable precisely because the barbarians are likely to plan and work together, at every level, so much better than civilised people. Barbary is about working together to survive, civilization is about complaining about taxes. (And the Romans had a lot to complain about.)
There are armies that take strongholds, like Caesar’s or Genghis’, and then there are brilliant armies that achieve nothing, like Hannibal’s or Attila’s. Caesar’s spade work is splendid, so he would actually do great in western Europe until about 1000AD, when stone castles started to reappear. Otherwise, some later Roman fortifications would be really tough.
All in all, it will always depend on what are the objectives, against who and where. Maybe against vikings. Of course, the vikings wouldn’t fight, they’d just take your silver and daughter and sail away. But one of the most significant problems would be the cavalry: if your cavalry is so weak it can’t even challenge the enemy scouting, you don’t know anything.