I've been having some idle musings about the Zwerchhau since it was one of the techniques I used most frequently back when I had a group to practice with and is still one of the things I drill most heavily in solo practice. There seems to be a general agreement that (for a right-handed swordsman) the Zwerchhau from left to right is done with the long/true edge since the version with the short/false edge is quite awkward. However, the Zwerchhau from right to left could be done with either the short or the long edge. I find both versions useful since they allow engagement at different range and leverage profiles, but I don't think I've heard anyone explicitly saying that they favour the idea of both versions being correct.

What do others think about this?

You mean a Zwerchhau from the Right Roofguard - vom Tag - to the left Ochs?
That is - at least in the way we train it and understand the texts - always done with the short edge.
If you strike like this with the long edge it is essentially a very horizontal Zornhau and makes the follow-up with another Zwerchhau - Umschlagen - a bit more awkward. Not enough to be really an issue when fighting - in free sparring you rarely get perfectly clean cuts anyway - but certainly noticeable.

We similarly always cut a horizontal Zwerch from right Vom Tag with the short edge - the cut is just as strong, the reach is just as good, and the body is coiled ready to return with a Zwerch from the left, or to wind and thrust as required.

Another way to think about why is that this Zwerchhau is basically just a transition from Vom Tag into Ochs, and we know from several sources that Ochs should generally be held with the thumb down*. If you want to have the blade in left Ochs with the thumb down, you must strike with the short edge to do so.

I would probably class a long edge 'Zwerch' from Vom Tag into a guard resembling left Ochs as just being a high mittelhau/oberhau/unterhau (as appropriate for the line your cut leads in on), since this angle means the followon plays of the Zwerch don't work as well, I think.

*If I recall correctly, Jud Lew says this, and PvD says to hold Ochs on the left with the long edge towards you, and Ochs on the right with the short edge towards you, which has the same result - keep the thumb underneath.

Hmm... From left to right, I almost always use long edge, mainly due to the awkwardness of the switch. It's almost, and probably better as, a Krumphau.

Still, if you are going to use it, it'd be sure that you can actually cut with it. Make sure its not just not getting the technique right, but if the move cannot be executed in a way that could cause damage, its not worth having.

I strike with the short edge when striking from my right and long edge when striking from the left, and when I want to strike from off my right side on to his right side I strike out with my long edge.