There's a place for all the different units, but it's knowing what that place is...
Cats are better for knocking down walls and slow units because of their extra damage and range, but they are easier for fast units to dodge because the stones are in the air for so long.
In theory, swords/legions should get beaten by missile weapons, but it doesn't always work. In one game I was playing Assy CA/HA v. a Choson sword/legion player. There was battle after battle between our towns, and he just had the upper hand. If I'd been able to tell my archers to always concentrate fire on the front enemy unit (and to retreat if they got too close), I might have won, but because of lag my orders always took a few seconds to get obeyed - so the swordman defence kept his town safe.
[Great game, but the stalemate in no-mans-land lasted for so many hours that in the end we had to call it a draw].CelticWarLord