Be aware:
120Hz HDTVs and 120Hz PC monitors operates differently. All HDTVs only accept 60Hz video inputs. 120Hz monitors accepts dual linked DVI-D (60Hz each).
120Hz HDTVs does internal video processing to insert frames to make movies play smoother and give the "live" like look. This causes input lag for gaming so you always want to switch to 60Hz mode.
120Hz PC monitors are refreshed by both DVI-D inputs so simplistically speaking, they can different parts of the screen are "refresh" between the two inputs. that makes for smoother gaming experience. This does nothing for movies to the best of my knowledge.