There is no max for the battlefield minus max unit size for 20 units. Technically you could have 4800 warband infantry in 1 army and the opponent having 4800 pikemen in there army, totaling 9602 men on the battlefield. Not very many comps are going to play that but I do'nt think there is nothing stopping that. But the game is programmed that if there is an army of 2400 men in an army 2400 in the enemy army and 2400 for reenforcements the reenforcements wo'nt come do to graphics/processing getting maxed out. It may vary from machine to machine where the cap is set at due to the game doing an analysis of your system. But from my experience it seems what would be huge battles is nullified when the cap is near met. Whe you are on the bordeline of performance the comp will throw in reenforcemnts right when the melee starts.

If ya really wanna see a performance drop. as soon as you have a bit of lag group all your units and put them on A.I. control. and you'll see snails moving around on the screen