Holding a long straight sword on a horse back charging fast toward your opponent, the window of striking the sword with its maximum and effective power is very small. The sword has to land with maximum blade contact. Assuming you are a highly skill swordsman and you make that small window, by the time the sword lands on its target the horse would have moved forward by a few steps. Retrieving the sword now becomes an effort as the blade is not parallel with the cutting line any more. This exercise becomes even harder if your opponent is not stationary and charging at you.
If you are holding a curved blade, depending on how it is wielded, the window of opportunity of striking with maximum power increases by a lot. This means an early swing or a late one wouldn’t have disfavored consequences. No matter which part of the blade strikes it will cut and will pass through the opponent quite swiftly.