Okay, caveat here is that I would play both of them in our strongest XI.
Roy
Root
Bairstow
Morgan
Buttler
Billings
Stokes
Ali
Rashid
Woakes
Plunkett
But in a straight pick? Bairstow has been averaging 70 in Tests, scoring quickly. He builds innings brilliantly, has all the shots. He has that bit more class than Billings.
Come on now, it's not a test match is it though

Take a look at their list A records, Bairstow isn't even close to Billings in limited overs cricket. Batting in mostly similar positions in the same competition, Billings scores faster, more heavily and at an average 15 higher than YJB, more tons in less games too.
Also Stokes at 7, Rashid above Woakes in the order, Willey dropped?
I'd bring Rashid back, Dawson to get a go for Moeen and obviously Billings in for the last game.