For me it would be bonefish. I like the whole sightfishing aspect: seeing, stalking, demanding casting, and instanf feedback on any of the many possible errors. The run is nice, but that and the subsequent fight is not the 'ultimate moment' in my opinion.
As to actually fighting a fish, I would vote for a billfish over a tarpon. I think both speed and aerials are much more spectacular with a marlin at the end of a flyline.