I played BF4 last night with my old PC that got me through BF3, thinking it wouldn't be much fun. To my surprise, it actually was a pleasant experience.
Phenom II 965BE oc'd to 3600
Settings in game defaulted to High at 1080p. I didn't look at all the particulars and didn't record the average FPS, but I'd say 40-50 FPS would be close.
Considering I'm using Vista and the latest drivers are from April (Vista is no longer supported by AMD), I'm pleased so far as the game was smooth compared to Beta. Each time the game started, a message popped up warning I had 13.11 drivers that would cause video problems and needed to update (duh). Tonight I'm going to try Windows 8.1 Enterprise and see if gameplay with the latest drivers improves things and fixes some of the glitches such as the console opening at will, although the cause of that is not clear. IIRC, BF2 had issues with custom key binds, but hopefully that isn't the case here.
What is becoming clear is a killer machine is not necessary to play BF4 like many, including me, thought. Before I build the new pc, I'll wait to see what other people are using and how well the game works for them. At this point I'm glad I did not build a new $$$ pc.
So my answer to the OP, based on my experience with an old outdated pc (admittedly tweaked and only slightly oc'd), is your setup shouldn't have any problems playing BF4.