More spokes = stronger wheel.
I don't think the different crossing patterns have anything to do with it. In general you want the maximum possible number of crossings on a rear wheel to make the spoking as near to tangential as possible. People will use fewer crosses on non-drive-side spokes, I think the idea is that since they are under so much less tension than drive-side, they don't transmit as much torque. (Hm...I have to think about that one....)
More crosses put less strain on the hub flange, but I think most hubs nowadays are approved for radial spoking. I've never seen a hub flange failure, but I've seen plenty of rim failures.
With a light aluminum rim, I would want 32 spokes for the rear.