You get symmetric equations for both fields if your magnetic dipole is built from north and south poles, instead of a current loop. Check Wikipedia's Internal magnetic field of a dipole.
Intuitively, with magnetic poles, the field inside the dipole is parallel to the (nearby) outside field, instead of anti-parallel; and that's the same situation as for the electric dipole formed by a positive and a negative charges.
As for the paradoxical case $-$ the spheres of current loops $-$ I believe that you have to take into account the energy of each electrical current $\mathrm{d}I$ under the magnetic field generated by the remaining of the sphere, $\mathrm{d}U = \mathrm{d}I\int B\, \mathrm{d}A$, in line with, e.g., Feynman's Lectures.