In theory yes.

The standard heavy cavalry unit, be they Cuirassiers, Grenadiers a Cheval, or Carabineers a Cheval tended to have a steel cuirass, a steel or bronze helmet, a large mount, and a long, straight sword, the Grenadiers a Cheval being the same except not wearing cuirasses.

So, a heavy cavalry trooper will be trained to use a heavy straight sword, which was meant for thrusting. Often these troopers would slash rather than trust, with Napoleon yelling at his heavy cavalry to trust, not stab at Wagram. As such, there is a reason to the stab, the slashing attack often only produced a superficial cut whereas a stab would go and pierce a vital organ. However the stab requires more effort than the slash, so many heavy cavalry troopers often took the easy way rather than the proper way.

Conversely, light cavalry were armed with light, curved sabers that were specifically produced for slashing and cutting attacks on enemies that were fleeing. As a result, they would have very little effect over a well armored heavy trooper.

So, in the end, a heavy trooper would have a natural advantage due to weapons, armor, and training.

/u/DonaldFDraper's comments aside, heavy cavalry was used to shock combat; heavier armour, bigger swords and larger horses statistically always come out on top in a solid clash.

What you're alluding to, I think, is the ability of heavy cavalry to act as an interdiction against cavalry in general. Any cavalry unit that loses its momentum and does not reform can be easily counter-charged by other cavalry (light or otherwise). Eg, the English heavy cavalry at Waterloo charged the French to great success but lost cohesion thereafter, enabling two smaller brigades of cuirassiers and 2 lancer units to rout them from the field, killing the English Union Brigade commander.

To literally use the idea of 'hammer and anvil' idiom, the heavy cavalry (the hammer) is not very useful if its not in motion.

I think a very important question needed to put this in context is:

What was the nature of cavalry vs cavalry combat in during the Napoleonic Era? Would we see formations of cavalry crashing into each other head on? Would the formations be loose enough for horses to pass by each other? Would it look more like a "Total War" cavalry battle or a "Mount and Blade" cavalry battle or something entirely different?

The convention was, certainly, that heavy cavalry, which by the Napoleonic era included dragoons (Dragoons, Dragoon Guards, Heavy Dragoons, but not Light Dragoons) as well as Cuirasssiers Grenadiers and Carabiniers, as previously mentioned, had bigger horses and straight thrusting swords, or heavy straight cutting swords, like British and Hapsburg heavy cavalry (the British heavy sword was a direct copy of the Hapsburg heavy sword). Light cavalry, Light Dragoons, Chasseurs, Hussars, Jagers, Chevaulegers and Lancers/Uhlans usually had smaller horses and curved sabres primarily used for slashing. Heavy cavalry sometimes had carbines or muskets, but light cavalry almost always had relatively effective carbines. There were national variations of course. Prussian dragoons started as heavy cavalry, but in the 1808 reforms pretty much became light cavalry, but without carbines, mainly because of the poverty of the Prussian economy at that point.
However, this was all theoretical, and by the early Napoleonic wars the differences, especially operationally, had become blurred. In Moreau's army in 1800 the regiments of cavalry, whether dragoons, chasseurs, hussars or cavalerie (heavy cavalry pre-cuirassiers) were used in exactly the same way, both for reconnaisance and as battle cavalry, all being expected to carry out all cavalry tasks, be it scouting or charging. Buonaparte changed this by amalgamating many of the Cavalerie regiments into the 12 cuirassier regiments, and then designating them as "Reserve Cavalry" and keeping them in brigades and divisions of Reserve Cavalry, whose purpose was solely that of carrying out decisive charges, and brigading chasseurs and hussars together as light cavalry to do the rest of the cavalry roles. Dragoons were brigaded together as a sort of less-expensive heavy cavalry, or perhaps more accurately as a kind of general purpose cavalry. However, although the Hapsburgs and the Russians similarly brigaded their Cuirassiers together as an equivalent of Reserve Cavalry, the Brits, the Prussians and Spain used their cavalry, light or heavy, pretty much as universal all-purpose cavalry. What complicates this further is that British horses were generally far superior to those of the French. Consequently, British "light cavalry" were better mounted on bigger and stronger horses than French dragoons were, even though French dragoons were regarded as quasi-heavy cavalry. At Sahagun British hussars rode over and through superior numbers of French dragoons, for example. Most of the time the advantage of heavy cavalry, such as it was, was moral rather than physical. Cavalry very rarely engaged in hand to hand combat, so the advantage of a cuirass, for example, although real if one is engaged in such fighting (Hapsburg cuirassiers fighting at Abensberg lost far more heavily than did the French because, it was said at the time, of the absence of a back plate) would mostly be one of creating an impression of power and strength. Ordinary cavalry, dragoons or hussars, for example, would be reluctant to cross swords with cuirassiers and would, therefore, rarely stand before them, still less attempt to counter charge, so the advantage would very rarely be one of superior heavy cavalry defeating lighter cavalry, but of heavy cavalry outfacing lighter cavalry.