This is a pretty aerodynamics question...

It is a fact that an airfoiled wing section can provide "greater lift" than a flat one (CL grows with airfoil thickness). For a stab this means IMHO that an airfoiled one can yeald a bit more pitch-"stable" airplane, in the sense that when the stab is seeing an AoA (for example, after a wind gust or so) it has a greater tendency to the equilibrium. Furthermore, another difference can be during snap rolls, spins - i.e. when the stab flies at high AoA - for the same reasons.

That said, it must be said also that in pattern planes the tail moment has a so great moment arm that small forces are needed to control pitch axis...

Moral of the story, IMHO: hard to tell the difference. For a beginner, I think that no difference could be noticed.