mATX/mITX boards aren't really stable for FX processors... you could do the Athlon X4 760k/FM2+ or you could go Intel...
the i3 is comparable to the 6300 until it gets into multi-threading, then the 6300 wins out by a decent margin... the i5 puts the 6300 to shame in all areas and competes with the 8320/50 until heavy multi-threading (53% faster single-thread, up to 26% slower multi-thread)... the Xeon/i7 are around the board faster...
If you don't want to overclock, then you don't need a Z87 chipset... the Xeon/H87 board is around the same price as a 4670k/Z87 with strong VRMs... generally you'll pay an extra $100 for Intel, but it'll be a little snappier in day to day activities...
.... or you can move to an ATX case and get a full ATX board... it's up to you... the FX 6300 and 8320/50 are great CPUs for price/performance, but AM3+ mATX boards don't have the power delivery to run without BSOD issues for the most part...
You don't need to go Intel, those are the people that think that if Intel has better top of the line CPUs (the i7 is better than the FX 8350 according to benchmarks, but in real life the difference is not that big), then they are the best choice at every price point.
There's one thing that the Intel fans are right about though: if you want to go mATX or mITX, then you have no decent options for AM3+ boards (unfortunately). If I were to guess, this is because the FX processors create a lot of heat, both directly, and indirectly, by drawing more power from the motherboard (more than Intel's offerings, anyway), which may cause issues in small factor cases.
As far as the numbers DrunkenPanda posted... take them with a grain of salt, it depends a lot on the benchmarks used and at what point in time the benchmark was ran.
On modern kernels like Linux (Windows uses the same kernel, Windows NT, since the late 90s) there is almost no performance difference between the FX8350 and the i7 4770k (this is not the case with Windows). And you have all virtualization options with the FX processor.
Don't get a Z87 board unless you need all those extra connectors or you overclock. If you don't have these specific needs, then all the other chipsets are better (they are cheaper because they don't have unnecessary features).
I'd wouldn't say Intel is just better till you get to the FX 9590 price point... which in that case, an i7 4770k is just flat out better...
I mean technically... if all you do is browse the internet and look at videos, check e-mail, and word process.... an i3 would be faster than a 8350... is the i3 as good of a processor? Not even close... but if you don't use anything multi-threaded, you'll notice the i3 to be snappier...
If all you do is game and stream, the 8350 would be a monster and an i5 would lag every once in a while...
So it all comes down to what you're doing with your PC and what your price point is that you want to look at... as far a price/performance goes, the FX 6300 certainly has more raw power than an i3... the 8350 has more raw power than an i5... but if you're not going to use the raw power for heavy multi-threading often (virtualization, streaming, video processing, etc), then the Intel models will be faster for what you're doing...
I'd buy a 6300 over an i3... an i5 over an 8350... but I really have no need for an i7/Xeon/8320/50
if you DO have a need for heavily multi-threaded tasks the 8320/50 spanks the i5...
however... seeing as how the OP needs a mATX board, AMD doesn't offer a lot as far as performance goes... I'd grab an i5/Z87 or Xeon/H87 (they're about the same price after you figure in mobo price difference) .... just decide whether you want to overclock (i5) or if you want hyperthreading (Xeon)
Note: gaming doesn't currently use hyperthreading... I can't speak for the future, I'm not Nostradamus...
You need a CPU with 4 cores for gaming (Battlefield 4 disable assets on processors with less cores, it is conceivable that other games might follow suit). For gaming, an i5 is plenty. So buy unlocked if you plan to overclock (you can go with the previous generation too, they overclock well, better than Haswell from what I hear), and locked if you don't plan to do that (Haswell, at stock clocks, are about 5%-10% faster).
As far as the board goes, if you don't plan to overclock, buy a B85 or a H87 chipset with a heatsink on the VRM (like this one: http://www.gigabyte.eu/products/product-page.aspx?pid=4567#sp).
If you plan to overclock, I am not knowledgeable enough to feel confident about recommending a motherboard (I am not interested in overclocking). As far as I know, overclocking gets you a few frames while gaming.
THere is just no good m-atx mobo for a FX 8 core cpu, but with a FX6300 you would be fine with an m-atx board. However rumours told me that msi is working on gaming series mobo´s for am3+ (included a m-atx) But like i said it are just rumours.
In my opinnion there are also ATX solutions for your space problem, some kind of cooler master HAFx desktop case.
Yeah confirmation on the throttling. With Prime95, the cpu gets to about 55*C and stays there, but is trottled from 3500Mhz to 1700Mhz intermitatently. Like few seconds on 3500Mhz, then 1/2 second of 1700Mhz, then a few more seconds of 3500Mhz, and cycles like that.
Of course...how real loads perform is very different. The CPU will OC itself to 3700Mhz and stay between 3500-3700Mhz if it has low core utilization. Totally worth it for $130 and that micro-atx form factor tho.