AMD processors are more than capable at gaming, you just need to buy the right one. Like Intel, AMD offer a variety of processors that cater to different uses. When you build a gaming PC, it's important to have a good balance of components. A blazing-fast processor will only get you so far if the GPU and RAM aren't up to scratch.
It's well documented that Intel processors offer better per-core performance than their AMD equivalents. Some people won't like to hear that, but it's the cold, hard truth. Naturally, you'll pay a premium for this, particularly if you go for an Intel processor that can be overclocked. On the other hand, every AMD processor is unlocked, meaning that they can be overclocked with the aid of a good aftermarket cooler.
To play BF4, you want either an Intel i5 or AMD FX-8xxx series processor (an FX-6xxx series will be fine if you're on a budget), but like I said, you also need to ensure you partner that with an appropriate amount of RAM and a good graphics card. 8GB of DDR3 1600Mhz and a GTX 760 will do nicely.