120Hz HDTV and 120Hz PC monitors are different.
120Hz HDTV creates an interpolated frame from every two actual frames it receives from the source (BL Player, DVD Player, PC) and inserts them in between each of those frames. This improves smoothness and makes movies look more "live". Since it takes time to create the interpolated frame, setting the HDTV to 120Hz actually creates input lag.
Input lag is no big deal for movies, but it can be a big deal for games. Unless the input lag does not bother you, you should always set the HDTV to game mode, or 60Hz.