>>Is the drag higher in the first case or in the second?<<
I've wondered the same thing. I asked a few aero engineers and the consensus was that there may be a difference in total tailplane drag depending on the type of trim system used...but that it was not worth worrying about.
Regardless of whether trim is being used or not, the horizontal tail surfaces are going to have to produce a given amount of lift. That lifting force will have a drag component, most of which will be "induced drag". Apparently, the effect of a displaced trim tab (in any type of drag) is negligible.
For a trim system that uses a trimmable horizontal stabilizer, I imagine the same is true.