I'd just get what's cheaper, especially that you're staying at 1080p. I have a 970 and it's performing very well at this res. Overclocked to 1506mhz it's not really that far off a 980 so I can't see how a 390 can be noticeably all-around faster.
The cards are practically identical performance wise but the 970 is the better clocker of the two. Plus, many games favour nvidia hardware.
Also, don't think the 8gb of vram is going to be useful on such a card. Both 970 and 390 can run out of grunt before using up all of their memory. People tend to overestimate the concept of vram and the reality is that you need a lot of grunt to properly utilise so much memory. You'd have to crossfire and I don't think you should bother with that as you can get a 980Ti for similar money and enjoy hassle-free gaming without any multi-gpu issues.
To sum up:
1. I'd stick with your 280x and wait for something better, neither the 970 nor the 390 are really worth buying new.
2. Get a used 290x/970.
3. If you have to buy new, get a 390. It's a good stopgap card till better GPUs arrive (and it's "newer" than the 970). I'd estimate you're going to get a year of gaming at decent details at 1080p out of it.
BTW, I'm using adaptive v-sync in gta and it works as intended so I don't know what some people are on about;p Also, I can comfortably use all Gameworks FX in Arkham City and maintain playable framerates. And yes, Nvidia drivers are still better. Had a lot more problems when I had an AMD card than I have now with the 970.
Having said all that, I'm waiting for a new card from AMD so I can switch just for the hell of it;p