Hi, Mike-
I'm sure that the plywood would be a lot stronger. The diagonal balsa would give some pretty good resistance to twisting torques, which is important, but going in only one direction per side, it might well contribute to fuselage warping. I believe that Larry Cunningham encountered that, after advocating the biased grain, and then rejected using it in only one direction. On the other question, such a thick piece of carbon would weigh much more than the balsa. You could probably anchor houses on such stuff.
I weighed some parts made with thin CF veil and FG layers filled with epoxy resin, and they were very light. The FG was a bit lighter in practice on a horizontal tail, probably because it absorbed less resin. A 2-layer CF veil test sample epoxied over 2lb/ft2 pink foam weighed about .008 oz/in2. I don't know how accurate it would be to say that one layer would weigh .004 oz/in2. That's pretty light for fuselages though. My old notebook, in which I list data from weighing my own stock, shows 1/64" plywood to weigh .0079 - .0087 oz/in2, or over twice as much as a layer of CF/resin as applied to the pink foam. The density of 1/64" plywood is twice to three times the density of spruce and about eight times the density of "average" (7-lb) balsa. The main point to remember when deciding among carbon veil, .56 oz glass, or similar laminates is that their weight is really negligable compared to the epoxy or dope used to fill them.
My rough calculations say that my current fuselage for a .25-powered stunt plane would have required 1.5 oz (not counting glue) of 1/64" plywood lamination, while the biased .56-oz fiberglas and epoxy added .25 oz to one such fuselage and closer to .3 oz to the other to cover about 7/8 the total side area (including cockpit) plus the fins, top/bottom, and cheek convexity. So, if you build light like Tom, the extra ounce wouldn't be a problem, especially for the stiffness and savings in labor. My total fuselage weight is about 5.9 oz. For comparison, the Cardinal ARC fuselage weighs 9 ounces, even with cutouts. So for larger fuselages, you're looking at a bit more weight difference.
The nice thing here is that with a little (relatively) easily measured data, you can approximate the weight gains from using various materials and make your best decision before building.
SK