They bench out very close, with each beating the other slightly in various test categories. The major pluses for each, outside of raw performance are-
970- lower power usage, quieter/cooler, better drive support from Nvidia.
390- 8gb of vram which helps at resolutions higher than 1080p.
Personally, if I was gaming at 1080p I'd take the 970 just for the support, if I was gaming above that, I would take the 390 for the vram. My 2 cents.