I want to throw in my 2 cents. Neither of those cpus are great, but both of them are strong enough for a R9 270x.
The i3 is superior to both of them for about the same price as the FX6300. The 860k is much cheaper than either.
Now if I HAD to choose between the two, I would choose the Athlon x4 860k every time.
860k pros-
1. Newer
2. stronger per core
3. much cheaper
4. Better memory controller
860k cons-
1. less cores
2. no L3 cache
3. already the best on it's platform
FX6300 pros-
1. more cores
2. higher potential
FX6300 cons-
1. weaker per core
2. OLD
3. runs like crap on sub ~$80 motherboards
4. much more expensive
Their performance is actually pretty similar overall, but the selling point for the 860k is it's SO much cheaper it's practically in a different price category. You can toss the 860k in a $50 board and it will work well, but you NEED to get a good board for the FX in order for it to run at full strength.
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($99.99 @ Newegg)
Motherboard: Gigabyte GA-970A-UD3P ATX AM3+ Motherboard ($76.98 @ Newegg)
Total: $158.97
vs
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD Athlon X4 860K 3.7GHz Quad-Core Processor ($70.99 @ NCIX US)
Motherboard: Gigabyte GA-F2A88XM-D3H Micro ATX FM2+ Motherboard ($50.99 @ SuperBiiz)
Total: $121.98
So if you choose to get the FX6300, that is the cheapest motherboard that I could possibly recommend for it. You will regret it if you put it in a cheap 780 series board.