Hi there first to answer your question no you won't need to upgrade your cpu.Now i have a few recommendations for you. When hd7770 launched, it was around gtx460 768 and hd6790 which are above gtx550ti, which is above hd5770/hd6770. It was a little slower than hd6850.
At that time, hardocp found that a mildly overclocked xfx hd7770 delivered the same game play experience as hd6870 and gtx560ti. See the article here:http://hardocp.com/article/2012/02/14/xfx_r7770_black_edition_super_overclocked_review/
If you read the BF3 page, you'll see hd7770 allowed them to smoothly frag people online on ultra*(fxaa instead of 4xaa, ssao instead of hbao, motion blur
off for both better frame rates and so they could see enemies better) at 1920x1200(~2.3mpixels). That was with launch drivers. 7770 is notably faster now.
They also overclocked the gddr5 quite a bit more, and you can too(this 128bit card can use all the bandwidth you can give it). A free program like MSI After-
burner will let you adjust gpu voltage to get the core past 1200(maybe 1250). Oh, can you give us more details about your Power supply? Brand, model, That will help us provide better suggestions of card to you.But gtx460 1GB is like hd6850 and gtx560 is like hd6870.If you want to spend more you can go with either a 7850($180) or 660($230)