Trimmable horizontal stabilizer (THS) and trim tab serve the similar purpose for two entirely different control architectures:
- Trim tab neutralizes the force on the pitch control for a reversible control system.
- THS neutralizes the pitch position (and, in the process, the force) for an irreversible control system (e.g. hydraulically/electromechanically actuated, analog or digitally commanded).
In the presence of an irreversible actuator, the actual hinge moment on the elevator no longer matters since the elevator position is being closed-loop controlled by the actuator (provided the actuator is sized correctly, of course); but more importantly, it is no longer felt directly by the pilot. Without this direct feel, a trim tab would be more than useless.
On the other hand, in the case of reversible control with direct elevator-to-stick linkage, deflecting the stabilizer would not allow the dual objective of maintaining trim and neutralizing hinge moment to be accomplished, since a TE up stabilizer would impart even more nose down stick force to the stick. The THS is equally useless for a reversible control for this purpose.
For this reason, I would be very surprised to see an aircraft fitted with both. But maybe there are oddballs?