Number one reason to use the diagonal 1x6 decking is because those will "snake" into spaces in attics that 4x8 or 2x8 or 2x4 sheets of Plywood will not.
Leaving a space gets you more "coverage" per board nailed down. Generally you want no more than 1/2 to 3/4" spaces between the boards. A spacer of that specific width makes your life fastening the boards down much nicer.
Personally, I like a self-drilling deck screw 2x long as the thickness of the planking. Using diagonal planking is good for not hiding the ceiling structure at all--which may be handy 10 or 15 or 25 years' from now if wiring needs to be snaked through the ceiling or the like.
The downside to any attic decking is that, if the ceiling is being used as the insulation plane, you are limiting the insulation depth to whatever the joist depth is. So, no cross-wise batts or another 8 to 16 of blown-in.