Well I'd keep in mind there are 4 levels of Billmen each with it's own set of armour and weapon upgrades.

I'd agree with the result when you tell me they were Bill Militia or even Billmen given it was 4 against 2 and your 2 Bil units were already reduced from killing the Generals body guard.

I'd expect Heavy Billmen to give any other Heavy infantry a run for their money. But please note...any dismounted Knight unit would be an ugly confrontation with the slight advantage being with the knights unit with all things being equal.