We study the gravitational radiation emission efficiency $\mathrm{\Gamma}$ of
superconducting cosmic strings. We demonstrate, by using a solvable model of
transonic strings, that the presence of a current leads to a suppression of the
gravitational emission of cusps, kinks and different types of loops. We also
show that, when a current is present, the spectrum of emission of loops with
cusps is exponentially suppressed as the harmonic mode increases, thus being
significantly different from the power law spectrum of currentless loops.
Furthermore, we establish a phenomenological relationship between $\mathrm{\Gamma}$ and
the value of the current on cosmic strings. We conjecture that this relation
should be valid for an arbitrary type of current-carrying string. We use this
result to study the potential impact of current on the stochastic gravitational
wave background generated by cosmic strings with additional degrees of freedom
and show that both the amplitude and shape of the spectrum may be significantly
affected.