I have done a few preliminary tests of SP and SAP vs CMAA.

In a third of the battles the SP lost, but not without making the CMAA pay. Losses ranged from half to double of the CMAA. The charge had no effect whatsoever (:eek:), in fact the CMAA killed about 3-4 in every charge while the SP killed 0 and only initially did the SP have the advantage. When the CMAA passed about 40 men left, the tide turned in almost all battles and they bit back (reason was the SP lost cohesion).
This was not what I had hoped for. Apparently the swords also get the +1 attack against pikes.
I proves it can pay to fight SP with CMAA at times, and even in equal fights as it is long and drawn out.

The SAP on the other hand kicked the CMAA all over the place. Got losses from as low as 5 to 21 compared to abnout 35-40 CMAA losses in general. Again the charge had no effect (even in Engange), despite it is of no less than 12 (chargebonus 4 + rankbonus 4 + melee 2 + rankbonus 2).
The reason the SAP didn't suffer was because it managed to continue its forward advance, something the SP didn't manage.