GTX 970 or RX 470-480?

1) CPU bottleneck:
This seems to confuse a lot of people. A gtx970 is not "a waste" paired with an FX-6300 because there are many games with minimal CPU bottleneck. The 2013 Tomb Raider is one example:
http://www.techspot.com/review/645-tomb-raider-performance/page5.html

In other games you may see over 40% higher FPS with a good GPU and recent i5/i7 CPU, but again it VARIES a lot by the game.

Future DX12 games will start to use the six threads in your CPU much better than they do know so you'll less of a bottleneck in many future games.

2) CPU bottleneck Part 2:
AMD's DX11 drivers are not nearly as efficient as NVidia's. So for games with a CPU bottleneck, the GTX970 is going to do better (relatively). Having said that, the RX-480 should do better in games that have minimal CPU bottleneck.

3) RX-480:
First, I'd get the 8GB version, non-reference such as Asus Strix (not 4GB, not reference).

We don't have all the RX-480 details but we do know:
a) much better DX12 support (when properly optimized for) due to ASync Compute, preemption etc than the GTX900 series and previous
b) 8GB VRAM is an option
c) VR support is better due to asynch time warp/preemption (though we don't know if there's a performance enhancement like the GTX1080/1070 has which can boost FPS by up to 1.6X due to rendering a single pass for both images)

d) other stuff: HDR, HEVC, higher bandwidth (all stuff for better monitors)
e) Freesync is cheaper than GSYNC (though still expensive. The one I recommend is $550USD. Asus, 27", 2560x1440, IPS). Note that not all Freesync works well. Must be at least 2.5X max to min (such as 30Hz to 75Hz range.) or there is no support below the minimum. Some are only 40Hz to 60Hz which is horrible.

Summary:
I'd wait for a good RX-480 8GB card.

Note that the consoles have a GCN GPU so game code is going to be optimized for this. In fact, the 2017, XB1 Scorpio appears to have an RX-480 GPU (as part of the APU). The new Polaris GPU's are slightly tweaked versions of the previous GPU's.

Now NVidia can and will have ways of performing tweaks so this is not to say that AMD is superior, just that the GCN architecture is in the current and updated consoles so there's an incentive to optimize for this now that DX12 is starting to allow more hardware level access.