Intel Core i5-760 vs AMD FX-8320 Eight-Core

Okay, this is how Motherboards and CPUs interact with eachother: The Socket.
That's essentially the only difference between an Intel and an AMD motherboard. However, it's a pretty big deal. That's because, as a general rule, a CPU won't be compatible on motherboard with different a socket type (However, there is some leeway when it comes to AMD. For example, there are multiple CPU types that fit the AM3+ socket).

Getting down to your specific hardware, your Gigabyte uses the LGA 1156 Socket. The AMD FX-8320 uses the AM3+. Needless to say, the AMD FX-8320 will not fit onto your motherboard.
(On a side note, the PCIe slot [PCI Express], is for graphics cards. Unlike CPU sockets, you can run almost every single graphics card out of any given PCI slot, just not simultaneously . This is because the PCI slots are all designed to be compatible. That said, a PCI 2.0/3.0 card will run into some bandwidth issues and run slower with a PCI 1.0, but it will still work. So that's what all that PCI jargon is about.)

Now, which CPU is better? The FX-8320 or your current i5-760? Considering you would need to get a new motherboard, the FX-8320's price suddenly jumps from $160 (Newegg) to $250 (because of the added cost of the motherboard). So the FX-8320 all of a sudden is looking like a very expensive upgrade for what I don't think will be that much of an improvement. (for your needs. I'm assuming you use your PC mainly for gaming?)

However, it does depend on what you want to do with your CPU. Are you planning on Gaming? Or multitasking CPU intensive processes like 3d rendering or video encoding? If you're planning on gaming, I recommend sticking with your current CPU and saving up to make a larger upgrade later (or upgrade your GPU or something). However, if you plan on doing a lot of heavy multitasking (when I say, "multitasking," I don't mean listening to music and checking your e-mail at the same time. I mean like, running another OS on two of the eight cores, encoding video on another, 3d rendering on three others and playing a game on the last two.), then you might have to make the upgrade.

When you do decide to make the upgrade, I suggest going the route of upgrading your motherboard at the same time. Your 1156 CPU Socket is essentially discontinued at this point, so the price of CPUs for your board are only getting more expensive.

The bottom line:
If you have the money to upgrade your motherboard and your CPU, and you have an installation disk of Windows for a clean install (You will need/want to do a clean install when switching motherboards), then by all means, buy the FX-8320. It's a darn nice CPU.
If you don't currently have the money, stick with what you have. It's still a solid quad core CPU.

You should also consider Intel when making your upgrade. There are some awesome i5s for gaming out there.

And take a look at the FX-6300. What's your Graphics card? It might be a suitable, cheaper alternative to the FX-8320. Just some food for thought.

I hope that helps answer your questions!

DonQuixoteMC