If both monitor and HDTV are 1920x1080 resolution then the FPS should be the same.
Make sure your HDTV is set to Game Mode or 60Hz. A 120Hz HDTV is not the same as a 120Hz monitor. 120Hz HDTVs only accepts 60Hz inputs. When in 120Hz mode, the HDTV's internal electronics creates interpolated frame in between every two actual frames and then outputs at 120Hz. This interpolation process takes a little of time and causes an increased amount of input lag which is a delay of when you enter a command (like moving forward) and when it is displayed on the screen.