what is the rest of your build?
Latest review with latest drivers that have been tested on the cards in your budget
I would expect the cards to give you about 25%+ fps due to fact the resolution in the test is about 25% more pixels than 1440x900
also expect more fps from all cards if playing in high settingshttp://www.hardwareheaven.com/reviews/1592/pg7/nvidia-geforce-gtx-650-ti-overclocked-graphics-card-review-battlefield-3.html
The giagbye and zotac are using 2GB vram and Evga is 1 GB, but Evga one is faster due to higher OC. This shows that VRAM size is still not a factor. The 7850 1GB is faster so not VRAM issue. Could be a memory bandwidthe issue since the 7850 1GB has more bandwidth but not sure.
$110 - 7770 http://pcpartpicker.com/part/xfx-video-card-fx777azdf4
$140 - 650ti http://pcpartpicker.com/part/evga-video-card-01gp43652kr
$160 - 7850 1 GB http://pcpartpicker.com/part/xfx-video-card-fx785aznl4
$180 - 7850 2GB http://pcpartpicker.com/part/xfx-video-card-fx785acnl4
$195 - 660 http://pcpartpicker.com/part/asus-video-card-gtx660dc2o2gd5
For your resolution I would be fine with the 7770 for high and 650ti for ultra. The 7850 1GB is only if you want constant 60fps at ultra.
For more future proofing or future 1080p, I would aim for the 7850 2GB or the 660, depending on how much you want to spend.