  In this paper we address the ratio of the shear viscosity to entropy density
$\eta/s$ in bosonic and fermionic superfluids. A small $\eta/s$ is associated
with nearly perfect fluidity, and more general measures of the fluidity
perfection/imperfection are of wide interest to a number of communities. We use
a Kubo approach to concretely address this ratio via low temperature transport
associated with the quasi-particles. Our analysis for bosonic superfluids
utilizes the framework of the one-loop Bogoliubov approximation, whereas for
fermionic superfluids we apply BCS theory and its BCS-BEC extension.
Interestingly, we find that the transport properties of strict BCS and
Bogoliubov superfluids have very similar structures, albeit with different
quasi-particle dispersion relations. While there is a dramatic contrast between
the power law and exponential temperature dependence for $\eta$ alone, the
ratio $\eta/s$ for both systems is more similar. Specifically we find the same
linear dependence (on the ratio of temperature $T$ to inverse lifetime
$\gamma(T)$) with $\eta/s \propto T/\gamma(T)$, corresponding to imperfect
fluidity. By contrast, near the unitary limit of BCS-BEC superfluids a very
different behavior results, which is more consistent with near-perfect
fluidity.
