In light of the fact that I seem to always end up playing factions for whom two-handed infantry is a notable part (Varangian Guard and Alamanoi, Zweihanders and such, Gotland Footmen and Sami/Norse Axemen, etc.), I decided to investigate their utility by running some Custom Battle trials:
First: Dismounted Feudal Knights vs. Zweihanders. Essentially, the two were evenly matched.
Next: A comparison of DFKs vs. Armored Sergeants, and Zweihanders vs. Armored Sergeants. The DFKs were overwhelmingly superior, losing seven men and killing 123, while the Zweihanders lost about 25 and killed about 75.
Now, I acknowledge that the two-handed axe units may perform better, particularly against more heavily armored foes, but I can't imagine that the basic message here would really change: Namely, that anything you can use two-handed units for, a relatively equivalent sword-and-shield unit can do it better (and Dismounted Imperial Knights can probably do it even better than that).
With that in mind, I'm wondering what uses people are seeing in two-handed units? Why recruit them or use them at all? On top of their unflattering performance relative to one-handed infantry, they're arrow-bait due to their lack of shield. Presumably they do have their uses... but what are they?
N.B. Anybody that says they're anti-cavalry units on the basis of "Bonus Fighting vs. Cavalry" is going to get smacked. If they can't take a charge without getting annihilated to a man (and they can't), they aren't anti-cavalry anything, I don't care if they are decent at fighting already-engaged cavalry.