Originally Posted by MisterFred
1) You can just use your AMD GPU with an Intel CPU...
2) AMD generally has more cores but significantly worse per-core performance in the same price range. This affects which company is better for certain purposes. For instance, many games can't utilize more than one or two cores, which favors Intel. On the other hand, the AMD fx-6300 is a price-performance beast if you need to do simple quad-core work.
3) When it comes right down to it, there is NO
AMD chip that's really competitive with the i7-3930k or the i7-4770k. Nor any that are as expensive. The latest ridiculous AMD processors are basically an fx-8350 overclocked to 5ghz. And it loses to an i7-4770k in most things.
For overall chip price, you really need to look at motherboard & cooling costs.
Example: an fx-6300 is an excellent chip which, when overclocked, performs well in all but the most demanding single-threaded applications. It only costs $115 or so. But you also need a $100 motherboard and a $30 or so cooler to get a good overclock without blowing out your eardrums with the stock cooler. So overclocked fx-6300: $245.
In comparison, you can get a locked i5 (Intel quad-core that can't be overclocked) for $210 or so and pair it with a $70 motherboard. In many cases that'll perform better than the overclocked fx-6300. Without having to go to the trouble of overclocking. At $280 combined costs. So there's a big rivalry there.
In that general CPU price range, the step above overclocked fx-6300 & locked i5 is generally an overclocked Intel i5 (followed by overclocked i7 if you have anything that needs an i7).
Stepping below the fx-6300/locked i5 you can go down to an Intel Pentium (dual-core) setup for about $140 total cost (CPU+mobo) or an AMD APU setup for about $180 total cost (this is still an excellent deal as it has good integrated graphics if you can't afford a graphics card.
Intel Pentium/AMD APU for $130-190 ish
Overclocked fx-6300/locked i5 for $240-$300 ish
Overclocked Intel of some sort for >$350 total CPU/Mobo/cooling budget.
Now I haven't mentioned some popular processor. For instance, the Intel i3 (no longer in a good price point since AMD cut prices on the fx-6300, so hardly ever recommended). Or the fx-8350 (for most purposes it's just not as good as an Intel chip. And in terms of cost, the fx-6300 is much cheaper, particularly given it's a rare application where 8 cores is going to make a huge difference over 6.
There are niche uses where you can consider other CPUs. But for your average user/gamer, you want one of the three price tiers I laid out above. What applications you use (specific games, work programs, etc)/whether you overclock makes the difference in terms of the specific recommendation.