I'm about 6' 3 1/2" and I went with S5. I am super leggy though...something like a 36" inseam. That means I don't carry as much of my height in my torso and I don't want to stretch my reach out too far forward. I also run a high rise bar so I don't have to lean forward as much. It makes climbing much more comfortable on my lower back, helps me keep my weight balanced going downhill, and helps me get the front end up more easily when I pull.
If you can ride both sizes, I'd try to do so and see what feels right to you. We are so conditioned to 'go by the numbers' these days, but comfort and confidence can only be assessed by being on the bike.
Also keep in mind that there's some adjustment built into these bikes. You could always play with your stem length, bar height, chainstay flip chip, etc. to dial in the bike's comfort. I can tell you that the high rise bars totally changed everything for me. Raising my hands just put me in a much more athletic, natural feeling position. I think all these things will vary by your body and how you ride though.
Another way to think of it could be...is it easier to make the S6 ride like a smaller bike if you need to adjust it to do so, or would making the S5 ride like a bigger bike be easier if you must?