I am looking for a physical interpretation of different behavior of electron and photon wave packets.

The dispersion relationship for a photon in free-space is linear ($\omega \propto k$), while for an electron (or any other massive particle) it is quadratic ($\omega \propto k^2$) (in free-space). If I form a (single) electron wave packet it will disperse in time (broaden with time of propagation), but a photon packet will not.

Apparently, any massive particle will behave the same way regardless of whether it has charge or whether it is a boson or a fermion. I would consider the dispersion relationship difference a purely mathematical explanation for this phenomenon, but is there a physical interpretation behind this?