What we do know is that kinetic energy adds mass as measured in the laboratory. So no the two situations are not at all alike. If related to quarks, then potentially, for example, there is a weakening of the intra-particle quark binding releasing energy and reducing mass while increasing inter-particle binding sufficient to oppose the repulsive coulomb forces, i.e. The nature and relationship of nuclear binding via interactions between the quarks in two different nuclear particles is (to my knowledge) not well understood, in addition to the unknown nature of coupling magnitude to the Higgs field. Second although one can speculate that mass is related to the Higgs field and in theory can give mass, the coupling constant between the Higgs and the electron and between the Higgs and the proton quark structure are selected, and there is no theory about the nature of the coupling between a particle and the Higgs field First the nuclear force is known not to be like a coulomb force.
In the nuclease there is not an attractive coulomb force situation but a tremendous repulsive potential energy. What we know about coulomb potential energy is that it does not have the property of mass.
The two situations are not at all equivalent as they involve two different forces. As you already mentioned, the kinetic energy is just 1/2 of the potential energy for electrons - the other 50% are emitted (usually as light), reducing the total energy content of the system. It is the same situation for both atoms and nuclei - you have an attractive force, you bring particles together and release energy corresponding to the lower potential energy afterwards.