heavy cavalry engaging heavy cavalry

[Urselius]

Not necessarily - a well-trained (in terms of unit training not individual skills) and well-knit unit could charge at speed equal to maximum speed of its slowest horse. In such case, a unit could keep its ranks close, no horse would be left behind. Modern horses can also be trained to "keep the line" even when advancing at high speed, as can be seen for example in the movie scene linked below (move to 5m 50s of the video):

Of course here you can see this in small scale, as only 3 horses are riding "knee-to-knee" in this scene. But if one line of 3 horses can do this, then lines of 6, 9, 30, 90, 180, etc. horses can do this as well, since as we know "management of many is the same as management of few. It is a matter of organization."

The extrapolation from the three horsemen in the clip to whole formations of cavalry is not as simple as you seem to imply. The three horsemen are stunt-riders on highly trained horses, the average cavalryman and mount of the past were probably less adept. No doubt the ground they were to gallop over was closely inspected to ensure that there were no obstacles, and there was not a rank of horsemen before or behind them. Also they were not being subject to missile fire (except for the man with a pistol firing blanks). I think a squadron of 100+ men in two ranks galloping at speed, trying to keep knee to knee over imperfect ground would quickly degenerate - with many falls and also injuries to riders legs from banging against a neighbouring horse's flanks.

Eylau was an exception, recognised as such at the time. Basically Napoleon had joined battle with too few of his infantry present, one infantry corps had been pretty much destroyed and his whole position was threatened with being overrun. The use of cavalry was a desperate measure, because he had no infantry left to stop the Russians. The attack was a prodigious success, mostly because visibility was bad and the Russian infantry had no time to form up to receive cavalry. It came close to disaster however, when Murat's cavalry had bulldozed their way right through the Russian army, the Russian infantry rallied and formed up between them and getting back to their own lines. On blown horses they would have been destroyed if the French Imperial Guard cavalry had not charged and covered their retreat.