A better way to phrase it might be the survival of short-tailed pterosaurs over long-tailed pterosaurs. (After all, anurognathids had short tails and appear to have lasted longer than other non-pterodactyloid clades.) Interesting that this happened in Avialae as well. (I have no idea if it's the case for bats, though.)
The mouse-tailed bats are extant. http://en.wikipedia.org/wiki/Rhinopomatidae Their thin and flexible tails don't seem to have an aerodynamic function, though, as far as I can tell. Those of long-tailed pterosaurs and eumaniraptorans, in contrast, are stiffened and have some kind of widening at the end -- though that was apparently vertical in pterosaurs and horizontal in eumaniraptorans.