Why is my sharp LC-50LB15OU 120Hz running on 60hz??

I cannot take credit for this because I just copied it from a previous post that is identical to yours. This will definitely give you your answer. Good luck!

The difference when watching a movie on your 120hz HDTV and the 60hz monitor is a separate comparison again. Your 120hz TV is actually creating frames that aren't there with its 120hz processing engine. With your 60hz monitor it is only showing the film in its original format, 24fps or 30fps. The movie will definitely appear smoother to anyyone watching it on the two screens as your TV is creating intermediate frames itself, which smooths out the motion. With a 120hz TV you also don't get any 'pulldown' in which certain movie formats can look like they pause fractionally every second.
Anyway, a gaming pc output on 60 or 120hz monitors is different kettle of fish as you are talking about the pure framerate the screen can display, not taking into account any kind of processing of the signal done by the display itself. Whether it is worth it to you or not comes down to
1: If you can you see a difference with the extra 60 fps? I'd suggest to try and have a look at some in-store or read a few reviews. (I saw X-bitsLabs reveiwed the Samsung 22" 120hz 1680x1050 monitor and sang its praises, saying the 120hz was very good.)
2: If your PC can do 120fps in the games you want it to? - I think with dual 5770s you will be close, depending on the game and resolution - check the charts on Tom's to get an idea
3: Will the games you play benefit from the extra fps enough to make it worth the money? If you are really into quick FPSs then you might find that 120hz really helps with gameplay, and you might be willing to compromise detail levels in the future or upgrade your gfx to get your 120fps if needs-be? If you play a lot of real time strategy games then 120hz may not be that important. For me I like eye candy and MSAA, and I play on a 22" 1080p screen so it looks super sharp with no jaggies. This drains every last pony from my 8800GTs in Sli so there are very few games that I would make 100fps in! For me 120hz wouldn't make sense without a big gfx upgrade.
You do have a PC with a good spec though, so if you have the money to spend then a 120hz monitor would be a nice thing to have, and it will give you an element of future proofing too, being 3d ready. You need to decide whether the benefits you will get personally will make it worth the cost.