The difference between AMD and intel for gaming.
Firstly, you need to decide what your priorities are, and what you will use the PC for.
Things such as: light gaming, heavy gaming, basic work (e.g. MS Office), heavy work (e.g. video editing, 3d modeling).
For the most part in current games the biggest difference will be made by the selection of the GPU. Get a great GPU + worse CPU rather than worse GPU + great CPU.
The AMD FX CPU's have
many cores, which are
weaker.
intel i5's have
less cores, which are
stronger.
The intel's consequently have better performance per core. In older games, the intels perform much better as those games are optimised for good performance with only a few cores (single-threading).
In newer games, the AMD FX's really shine due to the introduction of games using more cores (multi-threading).
The difference comes in depending on what you want to use the PC for. If you're on a tight budget, save some money and go with the AMD and spend the extra money on a better GPU that will give you better performance than any CPU could.
i5: Good for older games (single-threaded), Good for newer games (multi-threaded), Good for general work, great all-round CPU and probably the best around for current games (may change in future).
AMD: Slightly worse for older games (single-threaded), Great for newer games (multi-threaded e.g. BF4, Crysis 3), Good for light/heavy work, extra cores are great for 3d modeling and video editing or rendering, great CPU whilst costing much less than the intel. Even though it's worse in older games it will run them perfectly well and smoothly.
Regardless, both will perform well.
For an i5, I would recommend an i5 3570k or a 4670k. Why? They are king for gaming performance at the moment and since they are the k version they are unlocked and can be overclocked in future for a performance boost.
For an AMD, I would recommend a FX 6300/8320/8350 [
Do NOT go with a bulldozer CPU, only piledriver. List here: http://en.wikipedia.org/wiki/Piledriver_(microarchitecture) <-- That should all be one link, not sure why it splits.]. Why? Great multi-threaded performance for newer games and heavy work, are just fine in older games (not overkill, can deliver smooth frame rates maxed with a good GPU), and are great for productivity with a tame pricetag.
In conclusion, budget gaming/work: AMD. Not on a budget gaming/work: i5. The i5 currently delivers better performance but don't get the impression that the AMD is lagging behind. They are great for gaming and work with a really great pricetag, just not currently up there with intel. In newer games though such as BF4 the AMD's have caught up in performance and in some cases deliver better performance than the intel's for much less money. You will get great, smooth FPS with either.
Either solution will game just fine with a nice GPU, focus mainly on that.
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I would choose an unlocked FX over a locked i5 any day. Games are starting to use more cores so the FX is possibly better for the future, not to mention the socket of that i5 is unlikely to get any more updates and you'll have to buy a new mobo in future. Not sure about AMD, I've heard that the steamroller chips coming out will be AM3+ or FM2+.
PCPartPicker part list:
http://pcpartpicker.com/p/lNdG
Price breakdown by merchant: http://pcpartpicker.com/p/lNdG/by_merchant/
Benchmarks: http://pcpartpicker.com/p/lNdG/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($117.97 @ SuperBiiz)
Motherboard: Asus M5A97 R2.0 ATX AM3+ Motherboard ($94.99 @ Amazon)
Total: $212.96
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-14 14:23 EST-0500)
http://www.corsair.com/blog/ps4-xbone-pcgaming/
Overclocking the FX will likely bring it on par or further ahead than the i5. Both will perform great in games, focus more on your GPU.