That's a great PSU you've got there. Assuming you have a decent CPU too, the 970 or 390 are great choices.
Generally a 970 is great for 1080p. Big games like GTA5 & BF HL run great. There are some monsters like Witcher 3 which decimate even top end cards at 1080P Ultra. But usually that's a specific setting or (in Witcher's case it had a lot to do with Hairworks).
The first Tomb Raider (reboot) wasn't too hard on GPUs, except for TressFX. I'd be surprised if you had trouble on Ultra, though TressFX on Nvidia didn't work too well the first time around, so we'll have to wait and see.
You're asking me (and others) to speculate on an unreleased game, so I'm speculating... I *think* a 970 will get you 1080P ultra. And I'm *as sure as I can be* that if it's one of those few games that do bring top end GPUs to their knees, then there will only be a setting or two you need to drop to stay consistently at 60fps VSync. If there is a setting like that (TressFX, for example), then a much more expensive 980 or 980ti (or 390X or Fury/Fury X from AMD's camp) *might* give you the little extra horsepower you need to hold 60fps solid... but there's just at much chance that they still won't be up to it.
Look at Witcher 3 ultra benchmarks:
http://www.techspot.com/review/1006-the-witcher-3-benchmarks/page4.html
Minimum FPS are in the 20s for the best cards - they were getting smashed by HairWorks effects.
If you can wait for the game release and benchmarks, then you can make an informed decision. You may also have to wait a couple of weeks to see how driver updates and game patches impact on performance. But if you want to play it on day one, you'll need to speculate.
So you could get a 970 and you'll probably be able to run full-ultra, no compromises. OR, on the off chance that something like TressFX decimates GPUs, you could pay a lot more for a card which still only *might* handle the feature at a solid 60fps. For me, the 970 (or 390 - particularly given that it's a TressFX (=AMD) game), is a easy choice. I'm not prepared to pay a hundred Euro or more on the off chance that it allows me to turn on one extra setting. But it's your money.