Your question is really asks 2 things. A thick, symmetrical section for the stab as is used on most pattern planes has more and better control than does a flat plate section.

A lifting airfoil on the tail is completely different. On older free flights, the CG was way to the rear, 70% on the MAC in some cases, so the stab was in effect a rear wing, lifting upwards. Under power, the plane would climb, but would glide flat.

On a normal RC plane with the usual CG location, the stab force is downward. Have the stab come off in flight and see what happens. You get immediate pitch nose down. Use of positive incidence or a lifting section for the stab is an attempt to maintain level flight under changing power without changing trim. On a trainer, for example, you climb like mad with full power on a .46. The Telemaster series of planes has a flat bottom, lifting aorfoil on the stab. As power and speed increase, the plane would normally tend to climb. The lifting airfoil on the stab also generates more lift as speed increases, lifting the stab and negating the climb tendency.

Telemasters do fly around with their noses down and tails up in the air, looking stupid to my way of thinking. In my opinion, this is a poor design feature and adjusting the wing incidence does a better job and does not result in the nose down flight attitude.