I tried some custom battles, on a grassy plain with two handed units and here are my results:

French Voulge (510) vs. English Spear Levy (310) - French Voulge (note I kept them in the spear wall formation)

English Knights (530) vs. French Armored Sergeants (540) - English Knights

English Armored Swordsmen (610) vs. HRE Forlorn Hope (620) - Close victory by English Armored Swordsment

HRE Halbard Militia (300) vs. French Pikemen (240) - Crushing victory by halbard militia


From my tests it seems that two handed units are nearly equal to same cost units that are not two handed...
Note: No tactics were used just headlong collisions...