With a lance and spear, the momentum of the horseman is concentrated on the tip of a point, allowing him to plow through a formation effectively. How does this work when the horseman has swords or sabres only? Is there a 'shock' to the charge in this case?
I'm talking about cavalry from the Napoleonic era until the end of mounted cavalry.
There are two methods:
To hold the sword stretched out towards the enemy and try to skewer him. These swords were usually straight with a sharp point. This was the preferred method of most heavy cavalry units.
To cut or slash into the (most often) fleeing enemy. These swords were usually curved. This was the preferred method of most light calvary units.
Heavy cavalry units, for example cuirasseers, gendarmerie, heavy dragoons, etc, carried straight sabers, or sabers with a very slight curve. There charged into the enemy, hoping to cut them down before anything untoward happened to themselves.
Lighter cavalry units, for example hussars, light dragoons, etc, were not used as shock troops, but were employed for scouting, harassing and (hopefully) to pursue fleeing enemies. Their sabers were more curved. Makes sense, as their enemies were either fleeing away or they met on chance encounters. Their sabers didn't have to have a sharp point; no need for it as they usually slashed.
Later on the cavalry saber became straight and pointed, the more curved sabers disappeared. To finish off, there is little or no difference between charging with a sword stretched out or a lance. The point does the work. It's probably easier to work with a sword than a lance after the initial clash.
That is where cavalry experts differed in opinion: during the initial charge there is little difference between a lance or a sword point. A lance has the edge, as it is much longer. The difference came in what to do after initial contact. That's where the sword comes in very handy.
Lances were the cavalry weapon of choice when spears were the main anti-cavalry weapon. Swords were preferred after about 1700 when the main anti-cavalry weapon was the bayonet, attached to muskets.
Spears and lances were better against well-ordered infantry formations that existed before firearms. But "guns" tended to break up, or at least weaken enemy formations. Against "scattered" troops, swords or bayonets are more effective. The Romans knew that over 2000 years ago when they used throwing spears ("guns"), followed by a sword attack.
The idea of sword=based cavalry in the 18th and 19th centuries was to oppose sword to bayonet.The defending infantry had the advantage of firing their muskets to break up the cavalry beforehand. The cavalry had this advantage only some of the time, from their own carbines or muskets, or (seldom) from supporting infantry.