If your CPU isn't cutting it and you have a $230 budget to improve performance, by far your best option is this: i5 3470 for $200:
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115234
It'll drop in your current motherboard, no software/rebuild required.
You can't overclock it, but for most tasks it's faster than anything AMD has to offer even when OC'd.
Despite years of dual, quad and higher core CPUs, single-threaded performance is still hugely important. Intel is so far ahead of AMD in this regard which is why a dual core (4 thread) i3 can keep up with a (sort of) 8 core AMD 8350 or similar for lots and lots of benchmarks. If you have a particular application which runs well on AMD many-core architectures AND a strict budget, then AMD builds can make sense. But you already have the Intel Motherboard, chuck in the higher end CPU and be at least as fast (perhaps there will be a few specific scenarios where the AMD would be a little better), but in many situations it will be much better.
Plus you won't need an aftermarket cooler and you'll save on heat and power.