Some strange advice being given here. You are gaming at 1080p so that's the resolution to consider:
1. 3.5/4GB are both more than enough for 90% of games for this year and possibly the next.
2. AMD cards scale better at higher resolutions but at 1080p, the 970 is comparable with, if not better than, the R9 290X. See here: http://www.anandtech.com/bench/product/1355?vs=1056
3. Nvidia have superior drivers and support to AMD, whether that's worth a premium is entirely on you.
4. The 970 is better than the 290 at 1080p in almost every game.
5. The reduction in noise/power/heat output is not insignificant.
6. The 970 will have FULL support for DX12.
1. It's a relevant issue, maybe not very important but it's there.
2. It's been mentioned that the 970 is a bit faster (5-10%). Does that justify a 30-40% price increase and going over the budget?
3. So you say.
4. See 2.
5. Noise? The latest coolers are silent. As for power and heat, they've been mentioned several times.
6. Which means absolutely nothing at this point in time.