An answer that Professor Lenny Susskind gave to a non-physicist audience at Stanford in June 2012 went along these lines (by memory and some very short notes I took):
The charge on an electron is$\ \alpha \ \approx \ 1/137\ $which means
that 99% of the electron is just the bare electron while about 1% of
the time it is an electron plus a virtual photon.
Whereas the charge on a magnetic monopole would be $1/\alpha \ \approx \ 137$ so the
magnetic monopole would have about 100 constituents on average - like
lots of photons, current etc. Thus the magnetic monopole would be a
composite particle and very heavy due to all the strong fields and
Don't blame any errors on Lenny, it could be my mistaken memory/notes. I think that the dimensionless number $\alpha$ is a reasonable stand-in for electric charge since it is the coupling constant used to calculate connections between electrons and photons. Similarly, $1/\alpha$ would be the coupling between magnetic monopoles and photons.