With all the simulators I've ever used, it was immediately obvious from the word go that you were in a sim not in a real aircraft, purely from the handling and feel. That said, I don't think it matters as you're training technique and procedure, not finesse - in fact, it can be counter-productive to concentrate too much on minutiae that may be artefacts of the sim rather than characteristics of the real airframe.
I remember alternating between two supposedly identical (certified to same level) sims during a conversion course and one always gave you a perfect touchdown no matter what you did while the other felt like a crash every time. The instructors were aware of this so were just looking at technique and assured you that it would be OK in the real thing.