I'm not sure what the aerodynamic pros can cons are, but having flown
well over 100 hours in Pipers and much more in Cessnas, I haven't seen a
huge difference. The biggest difference I've seen in the Arrow I fly
now as that almost as soon as it touches down you lose a fair bit of
elevator authority and it tends to drop the nosewheel a little more
harshly than I prefer. None of the Cessnas I've flow had the tendency.
The nose would gradually drop with airspeed during the roll-out.

I suspect, but don't really know, that the placement of the main
undercarriage is a greater factor in the effect than the stabilator. I
vaguely recall that Piper took advantage of the greater control authority
possible with the stabilator to install a slightly smaller horizontal tail
surface on one or more models--although I thought that it was the Archer.

The PA-38 Tomahawk, which had a Tee mounted fixed stabilizer and moveable
elevator, exhibited essentially the same trait. If you held the nose off,
it would drop rather precipitously. It also had the main undercarriage
mounted farther aft than a Cessna of similar weight--presumably to prevent
tipping the aircraft on its tail when the boarding step was in use.

The high wing Cessnas faced no such consideration, and the nose wheel could
be held off much longer and dropped more slowly.

Peter