All 3 CPUs mentioned would play BF3 smooth, but the 7770 wont play it smooth on high settings unless you have a lower resolution monitor. The 3570k is the better of the 2 CPUs.
To give you an idea of performance here is a chart.
According to this, at 1920x1200 with 4xAA the 7770 is slightly slower than a 465 which is what I currently have. My card is OCed to about 480 speeds and at 1920x1080 I play medium to high settings with 2xAA and High post AA. I average about 40fps with this card and a 2500k. With the 7770 you will probably average a bit less depending on settings and resolution.
"Resolution is just a number." #Ubisoft Origin/Steam
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