Even if the HDTV says it has a refresh rate of 120 more then likely it is only 60FPS. Those "extra" frames are created by the HDTV to give the picture a clearer look. Your best bet is to use V-Sync to cap the game @60 FPS, that should be smooth and not have screen-tearing issues.
EDIT: You will also want to turn off the clear-motion (or w/e its called based on the company) that disables that higher refresh rate.
The way 120hz is done on a tv is with interpolation. This doesn't work with games. Basically your tv is a shitty 60hz monitor with high response time, high latency. Yes if you render more than 60fps you will get vertical tearing just like if you did and your monitor only did 60hz.
Like I said before it's just like a 60hz monitor with high response times, and high latency.
Response times and latency are measured on monitors, you don't get to know these most the time for Tv's. Most the time they are horrible.
In other words
skyrim = fine
first person shooters = bad