Nvidia released new drivers today (5/2/2016) in support of new titles including Battleborn. GeForce Experience didn’t find them so I downloaded them directly from the site:
They are numbered 365.10 and are WHQL (for those that don’t know, WHQL means they have gone through Microsoft’s approval system and while that doesn’t guarantee they will be free of flaws it is a good sign )
If you aren’t having performance issues you might play it safe and stay with what you have. I do install the latest myself - but that’s just how I roll ; waiting a week or so to see if others have issues is probably the better thing to do. If you are having issues there is a very good chance these drivers will clear them up.
AMD hasn’t released drivers that specifically mention Battleborn, but they did release new drivers a few days ago which can be downloaded here: