Hi William.....
As I see it, a pivot point could have a positive stop without any play, whereas a sliding mechanism must necessarily have some play to allow the the headstock to slide freely. Unless there is a way to take up the play evenly when it's locked down, there will always be that amount of play that will interfere with it's registration with the tailstock.
A pivot point with a positive stop is limited only by the amount of play in the locking mechanism, plus any play in the pivot point itself.
By virtue of design, the possible error is less than a sliding mechanism.
Certainly, I'm speaking of theory here, and if the play which allows the headstock to slide is only a matter of a few thousandths, then my point is insignificant. As a practical example.....while using my tailstock (which slides similarly in design to a sliding headstock), I do twist the tailstock in a clockwise direction prior to locking it down, and thus eliminating any inherent play. When I do this, it does align with the spindle more precisely. It probably wouldn't make any difference at all in a "real world" application, because the movement is only a few thousandths.
When both the headstock and tailstock have this sliding design, then the possible registration error is compounded.
-----odie-----