Well BF3 is generally considered a well optimized game and Hyperthreading gives anywhere from a 7 to 10 fps boost with a an i7 3770k. It's an even greater help with i3's, where hyperthreading almost gives up to a 15 fps boost.
Here's an article where the tester runs the game with HT on and off on a i3 and an i7. Look how much HT helps :D
http://chipreviews.com/main-feature/main-news/battlefield-3-revisited/4/
However, in this test, HT only seems to benefit at stock clocks. Later in the article he tests at various overclocks and the more you turn up the 3770k, the worse HT works on Frostbite.