This is game dependent. However you should exceed 60FPS most of the time with games at medium settings @1080p. There are some GPU heavy games that may not stay above or at 85FPS all the time though even with medium settings. Ultimately if you are consistently above 60FPS most of the time, then you should have a smooth gaming experience even if you can't maintain 85FPS all the time.
The 970 is an excellent card for 1080p gaming, and some games it works well up to 1440p.