Way outside of my realm here, but I think belts are more efficient than shaft drive. Far more load bearing surface contact and less redirection of forces. So long as the belt is strong enough to handle the forces and isn't too tight or too loose, the belt should be more efficient. A shaft turns rotation in one axis to rotation along a second axis, back into rotation on either the same or different axis as the first. The load bearing surfaces are usually a couple/few teeth of a gear and that's it. Helical and herringbone teeth can increase the surface contact and make for a more efficient power transfer, but on these helis the belt is making contact with over half the sprocket and the force is transmitted with a twist of the belt, effectively no redirection of force unlike the two or more redirections needed with the shaft drive.
That said, I may be wrong. All that belt contact with the pulleys may incur a heavy friction loss. Belt material bending around the pulleys may also incur significant frictional losses. Getting the tension in the sweet spot may be trickier than I think. Even with proper tensioning the longer the belt the more chance for flopping and harmonic vibrations that can sap the system of power.