I bought a Sapphire 7790 in September in preparation for BF4.
PSU Corsair CX430
Intel Core i3-2120 2 3.30 Ghz
6 GB Ram
I've been playing Far Cry 3 at high settings, no problem. Unfortunately, in Battlefield 4 I have a very low framerate and experience lag every 5 seconds or so.
I'm pretty sure I have the latest Catalyst drivers, as the website says they were released before I bought my new graphics card (and installed drivers for it).
I will be patient for patches and new drivers, but I'm disappointed the game is not running well at all, even in Test Range and single player.