Even though it sounds rather one-sided being the 2nd in charge of a heavy cavalry regiment, but to me it seems logical that heavy cavalry is, in the view of utilitarianism, the best cavalry (or 'was', either way). This because of the advantages they have. heavy cavalry would in most occasions beat infantry and cavalry alike when engaged 1on1 (of course in an ideal situation; a perfect 1on1 situation). Of course one could argue that having light cavalry is more useful because of faster movement & hit and run situations, adding a tactical advantage, and that lancers have the advantage that they can deal heavy blows in a charge vs cavalry and infantry. But in the end the heavy cavalry is that which can fend most for itself, granted not entirely, you'd always need support in a cavalry charge, but they can take the hardest hit, were in most cases most intimidating and dealt the heaviest blows because of their main (obvious) aspect, being heav(ily armed).
Of course it can always depend on the situation that you have, when odds aren't ideal you might require other cavalry. But I can only imagine that if you had a perfect 1on1 situation, heavy cavalry would be the most effective.
Having said that, I am aware that an ideal tactical situation nearly never occurred, so historically speaking i'm probably wrong, practically speaking though, that is my reasoning behind it.
It is rather apparent that you lack historical knowledge when it comes to cavalry, i take it you are basing your statement off of ingame knowledge.
It is well known that, no matter the size of the sword or being dressed in iron like a turtle, that to wininning a cavalry engagement it is all about organization during the charge. The side who keeps it's ranks the best dressed in the highest speed during the charge is the side that will win. This is apparent when you have 2 squadrons of (Hungarian) Hussars beating two regiments of Carabiniers at Leipzig 1813.
Another thing you fail to realise is that 99% of the time when infantry formed a square, that square would hold and the cavalry would run off. Only if you caught the infantry out of square were you able to rout them with cavalry, but by that stage it doesn't matter what kind of cavalry you have, whether it be light or heavy. However light cavalry often had much more gifted riders, and had could travel faster (albeit not by much), giving them an advantage when it came to exploitation and surprise.
Further defiecencies in heavy cavalry is that it cost a load for horses an equipment when compared to a dragoon, or even a hussar, despite their fashion needs. Lancers are the cavalry that have the most advantages, however it is difficult to get a sufficient amount of well trained lancers since a lance is a weapon that requires a great deal of time to master. However when you get people who have mastered the weapon, you will end up with a force that can be used for reconnaissance and scouting, doesn't cost much for equipment and horses, has better mobility and range on the battlefield. Another thing i wanted to point out is that, by rolling your greatcoat and putting it over your torso, you have essentially made a cuirasse that is invunerable to sabre slashes.
So even in your perfect 1v1 situation, if heavy cavalry was pitched against lancers they would have no advantages since: Lancers will have superior shock on the charge which is all that matters, the side who deals the most damage in those first few seconds has almost always won the engagement.
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