OK, I know a lot about this from carpentry, not rockets or airplanes, but, I kinda think that plywood is plywood? So, yes, the grain alternates direction on each layer. Therefore, in order for the face grains to be parallel, there will be an odd number of layers - always. And, therefore, there are more plies oriented in the face grain direction, so, yes, there will be more flexibility across the face grain than along it. You can easily feel the difference if you have a sheet of 3 ply, 1/8" light ply from Balsa Machining, just bend it with your hands and the difference will be obvious. Possibly more importantly, in structural materials each layer contributes strength in proportion to it's distance from the chord line - like in an I beam, the top and bottom plates are the strength, the middle plate mostly serves to hold the top and bottom away from the chord line. So, the face grains, being farther from the center of the sheet contribute more to the strength of the sheet than inner layers do.
tl;dr - plywood is much stiffer along the face grain than across it.