Actually, scratch that. I'm doing it now with 500 vs 500 and the spearmen are using their spears a lot. Some switch to swords. I'm guessing the latter are the ones doing the damage.
EDIT: Nope. Once they're engaged, it looks like vast majority of the spearmen have switched to their sidearm.
EDIT#2: So I did all the factions as 500vs500. Here are the results.
Sturgian Spearmen vs Sturgian archers:
Lost, 479 dead. Won, 365 dead
Sturgian Spearmen vs Aserai Archers:
Lost, 485 dead Won, 289 dead
Sturgian Spearmen vs Vlandian Hardened Crossbowman:
Lost, 484 dead Won, 282 dead
Sturgian Spearmen vs Battanian Hero(gee I wonder what's gonna happen):
Lost, 481 dead Won, 138 dead
Sturgian Spearmen vs Khuzait Archer:
Lost 481 dead Won, 256 dead
Sturgian Spearmen vs Imperial Archer:
Won, 268 dead Lost, 474 dead