I’ve got a LightBicycle carbon fat bike rim that has drilling staggered so that the holes are 9mm either side of the centre line.

Do I go for shorter spokes to the same side of the rim as the flange or use slightly longer spokes and cross them to the opposite side?

This site http://www.troubleshooters.com/bicycles/wheelbuilding/ says;

Notice that every other hole is offset to the left of the center circumference, with alternating holes offset to the right. It’s ABSOLUTELY essential that spokes from the left hand hub flange go to left-offset rim holes, and spokes from the right hub flange go to the right-offset rim holes.

If you were to do it the other way, spokes would cross the center circumference, with each spoke entering the rim at an unacceptably shallow angle rather than the preferable 90 degrees (perpendicular).

The necessity of not crossing the center circumference constrains your wheel building possibilities.

but I read elsewhere that crossing them would build a stronger wheel (but a bit heavier due to longer spokes).

What would stw do?

Don’t cross the spokes. There’s absolutely no need and fatbike wheels have managed without it for years.

I crossed a build once, it was weird to tension & build.

Don’t bother.

cool, thanks both.