Suppose you have an ideal mirrored box that contains enough photons as to have a relativistic mass equivalent to the [rest mass + kinetic energy] of an electron. In other words, the two systems have the same total energy.
How would I distinguish these two systems? They have equivalent gravitational pulls and I believe they have equivalent inertia. Are charge and spin the only distinguishing factors (I'm assuming the "box" itself has no properties of interest)?