This topic historically gets into a pi$$in' contest between those that say that anything other than a flat plate stab (for small models) is a waste of time and those (like me) that advocate built up, airfoiled stabs. Everything I design & build lately is for 1/2A power and I automatically try to use a symmetrical built-up stab whenever possible. Personally, I think I can "feel" the difference in the flight characteristics of the 2 types and enjoy the smoothness and predictability in pitch I think I get. Can I prove it with bags of numbers and equations? Nope.

One thing though, isn't a stab just a small wing? Can one tell the difference betwen an airfoiled wing and a flat plate wing? Methinks you can. And yes, before someone jumps in and shouts that flat plate foamy planes are a superior concept, I have flown them and they fly pretty good!

As far as what airfoil sections to go with; conventional wisdom calls for an NACA0009 or 0010 but one of my favorite, best-flying planes has an Eppler 168 stab which is 12.44% thick. Go figure. The thickness was needed to fully enclose the twin rudder bellcrank & pushrods.

I haven't done a built-up, airfoiled vert/stab yet but I think they should be superior in the yaw axis as well. Just my opinion, YMMV.