120Hz HDTVs work differently than 120Hz PC monitors.
To put it simply, 120Hz HDTV creates extra frames to make videos look smooth and also give that "live-ish look" like a news program or soap opera. Creating these extra frames takes time and increases input lag; the time it takes between you making a move or firing a gun and when it is displayed on the screen.
For gaming on a HDTV you always want it in 60Hz mode.