One problem with the FX CPU's is they tend to have a much lower MINIMUM frame rate which can be very obvious at times. Even if you find the right combo price that showed the AMD setup got a little higher frame rates I don't think I'd recommend that.
Another issue is that a slightly better Intel CPU with higher cost might last a bit longer when you likely find the money to get a better graphics card in two years. Of course that's a little less budget now for the graphics card so it does get a bit tricky, especially considering some games will run BETTER with more GPU power, but others will run better (at least less stutter) with the better CPU.
I could also help a bit more if I knew the TOTAL BUDGET as it sounds like you're building a new PC. I like pcpartspicker .
My advice would be:
That's $400 almost exactly. Even though an FX-6300 can be found for $60 cheaper and it's tempting to recommend it you might want to calculate as a PERCENTAGE how much that $60 works out to be over a three-year period when you add up your:
b) Network costs
It really is difficult to compare though. On one hand that's $60 more for a better graphics card, on the other hand the minimum will be lower and future upgradability isn't as good due to that (a bottleneck remains a bottleneck.)
I don't want to start a war here though.
I don't know if I helped or no, I'm just trying to give you enough information to make an informed decision.
Get the fx-6300 gtx 760. In most games that aren't super cpu intensive the fx-6300 is very close to the i5. Since the 760 is better than the 7870 you'll see more fps with the 6300 and 760 than the 3470 and 7870