A 3D HDTV operates differently from a 120Hz PC monitor that can used for 3D gaming.
HDTVs only accepts 60Hz input while a 120Hz PC monitor can accept 120Hz input. That means playing games in 2D mode will be limited to 60 frames per second on a HDTV and 120 frames per second on a 120Hz PC monitor. Cut that in half for 3D gaming since each eye will only receive half of the frames.
Also, on a HDTV you should always set it to "Game Mode" or 60Hz. Otherwise, the HDTV will create an insert interpolated frames. This is good for movies and videos since it makes the playback look smoother, but it is bad for games because it creates input lag.