heavy cavalry engaging heavy cavalry

[Robert Vermaat]

It does have some relevance. Generally speaking, the Romans trained their cavalry in Alan tactics. Horse Archers, like the Huns, would break and run when being attacked by well-trained lancers like Alan Catafractarii, but lesser trained lancers, like most Roman cavalry, would break when attacked by Huns.
On the notion of pistols, the Romans did have arcuballistae, which could be fired one handed.

Even so (and I fear that you may have been thinking of recent depictions of small ballistae in Hollywood movies), these weapons are not in any way comparable to early pistols or other firearms. Besides that, we have no evidence of them being used by Romans in any simalar massed way.

To those who have indeed tried to create a relevance between Ancient heavy cavalry against heavy cavalry, I say Good job! To those who continue here to mainly show off their knowledge about post-Medieval cavalry, but without attempting to do the same about Roman cavalry, I say Please read a book on Roman cavalry issues, in order to make this a relevant discussion that does not digress on every page towards modern issues.
There are several experts on Roman cavaly on this forum, yet none of them are engaging in this discussion, which is a real shame.