This paper provides a thorough, parametric comparison of axial and radial flux coaxial magnetic gears with surface-mounted permanent magnets. While both topologies share similar operating principles and can achieve comparable shear stresses, they exhibit different scaling trends with respect to key design parameters. Both topologies’ volumetric torque densities (VTDs) increase with the outer radius, but the axial flux topology's VTD increases with the radius at a much faster rate than the radial flux topology's VTD. Another difference between the topologies involves their cross-sectional scaling parameters. The stack length axially scales radial flux gear cross sections, and, as it increases, the impact of end-effects decreases, which improves the performance. For axial flux gears, the radii ratio scales the cross section's radial width between different radii. This fundamentally changes optimal parameter values and design performance tradeoffs. Finally, axial flux rotors experience significant axial forces, but the radial forces on radial flux rotors can be balanced out. Based on these trends, radial flux gears are superior to axial flux gears for most applications; however, axial flux gears have a significant advantage when a large radius and a small axial length are permissible or when mechanical power needs to be transmitted across a flat barrier.