Longsword is longer and deal more damage than the ACS, and it's arguably a better choice when you get dismounted too. However, you do sacrifice the shield for it, and as cavalry the shield is very important. Don't get me started on morningstar, if you want to hit unaware enemies or charge into mass melee with heavy horse and heavy armour that weapon is a true beast.
Still, I think 1h cav is better as ranged is less of a threat.