Yes, I think Mount and Blade is much more realistic for this, even though it's mainly on a smaller scale.
The whole point of cavalry is their incredible mobility, so I agree it's not very realistic to show cavalry always just sanding there and duking it out, though that did sometimes happen (and was a tactic for certain types of 'heavy' cavalry in the 18th and 19th Centuries)
More generally though, cavalry warfare is all about achieving local numerical superiority. Your enemies forces are positioned just so, stronger here, weaker there; more organized in this place, less in the other... up against a natural obstacle like a stream or a hillside in one place, or out in the open on the other.
Cavalry can suddenly concentrate forces where the opponent is weakest. On a smaller scale this can be as simple as a string of enemy soldiers, and the cavalry sweeps down on the tail end of the column and gangs up on the few guys there just long enough to do some damage, then sweeps away again before strong opposition can be organized. On a larger scale, an army can be caught for example while they are crossing a river, with half their forces on one side and half on the other, one side struggling with the baggage train and one ready to fight. The cavalry can go for the former and wreak havoc.
For this reason, situational awareness, battlefield communciation and battlefield intelligence are extremely critical for cavalry warfare. It's why cavalry uses flags, bugles, drums and so on to coordinate their activity. This is where the Mongols, for example, really excelled. They used whistling arrows, flags, and so-called 'arrow riders' (couriers) to communicate, and were really superb at detecting weakness in their enemies armies.
Long range missiles can help create these weaknesses, which again is one of the ubiquitous tactics of the Central Asian steppe, and the Mongols, Ottomans, Mughals, and various nomadic groups thereof. Flight arrows rained down from a distance could create panic among enemy fighters (and their horses) which the Mongols could practically smell...
Many of these tactics, like the couriers and signalling arrows, were quickly adapted (or maybe they already existed and were re-emphasized) by Europeans who had to face Steppe Nomads, particularly in Poland and Hungary, who adapted both light cavalry of the Central Asian style and the heavy cavalry . The Czechs went the other direction and emphasized infantry with war wagons and crossbows (later guns) which properly coordinated, could resist and annihilate cavalry charges.
The charge of the heavy cavalry is also part of cavalry tactics, and it comes at the wavering enemy line, it's a more decisive move, but has always been part of cavalry tactics and actually also originates on the Steppe - the Scythians and Sarmatians had heavy cavalry. This was something the Europeans really perfected, though against more sophisticated cavalry they had to learn to put this type of fighting in it's place.
The other big factor in cavalry warfare is morale. Infantry tends to be more steadfast. A lot of cavalry fighting involves mad chases, confrontations, deceptions, backing down, regrouping, false retreats, sudden splits of formations and coordinated maneuvers... the outnumbered side suddenly becomes the larger force, and vice versa. The morale of both the riders and their horses can suddenly fluctuate, a sudden fullisade of guns, a steady rain of flight arrows, enemy maneuvering which looks like it's cutting off hope of escape. Many cavalry battles seem to hinge on sudden changes in morale. This is why strong personal leadership can be so important, which in turn is, I think, why the best heavy cavalry comes from feudal aristocracies; the best light cavalry from nomadic tribes, and the best infantry from republics.
G