First major upgrade, not sure if AMD or Intel

[FoxingtonTrot]

So I am overhauling my system for the first time and am not quite sure which brand of processor to go with. I want to be able to play BF4 decently (maybe medium-high settings at a solid frame rate). All I want to purchase for now is a new CPU/Mobo/Ram. The video card I currently have is a Radeon HD 6950 1GB. I'm not really sure if my goal is even possible with this GPU paired with the following hardware, so let me know. Also please tell me if any of my choices are not great and what else I should go with given these price ranges. I would rather not go over $400 with this upgrade. Thank you for any help!

Possible AMD option
AMD FX 8350 $200
asus m5a97 r2 $94
Team Vulcan 8GB DDR3 $50
Possible Intel option
i5-3570K $200
ASRock Z87 $120
Team Vulcan 8GB DDR3 $50

 

[lowerCamelCase]

What case do you currently have? Does it have front USB 3.0 ports, and what ATX forms does it support?

 

[FoxingtonTrot]

What case do you currently have? Does it have front USB 3.0 ports, and what ATX forms does it support?

its a NZXT Apollo no 3.0 front ports. Specs say ATX, Micro-ATX, BABY AT for Mobo compatibility

 

[lowerCamelCase]

I'm not sure about compatibility with your video card as I couldn't find the one you're talking about.

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-8350 4.0GHz 8-Core Processor ($189.99 @ TigerDirect)
Motherboard: Asus M5A97 LE R2.0 ATX AM3+ Motherboard ($79.99 @ Microcenter)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1866 Memory ($93.22 @ NCIX US)
Total: $363.20
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-12-01 09:17 EST-0500)