  In this paper the low-temperature properties of two isostructural canonical
heavy-fermion compounds are contrasted with regards to the interplay between
antiferromagnetic (AF) quantum criticality and superconductivity. For
CeCu$_2$Si$_2$, fully-gapped d-wave superconductivity forms in the vicinity of
an itinerant three-dimensional heavy-fermion spin-density-wave (SDW) quantum
critical point (QCP). Inelastic neutron scattering results highlight that both
quantum critical SDW fluctuations as well as Mott-type fluctuations of local
magnetic moments contribute to the formation of Cooper pairs in CeCu$_2$Si$_2$.
In YbRh$_2$Si$_2$, superconductivity appears to be suppressed at $T\gtrsim~10$
mK by AF order ($T_N$ = 70 mK). Ultra-low temperature measurements reveal a
hybrid order between nuclear and 4f-electronic spins, which is dominated by the
Yb-derived nuclear spins, to develop at $T_A$ slightly above 2 mK. The hybrid
order turns out to strongly compete with the primary 4f-electronic order and to
push the material towards its QCP. Apparently, this paves the way for
heavy-fermion superconductivity to form at $T_c$ = 2 mK. Like the pressure -
induced QCP in CeRhIn$_5$, the magnetic field - induced one in YbRh$_2$Si$_2$
is of the local Kondo-destroying variety which corresponds to a Mott-type
transition at zero temperature. Therefore, these materials form the link
between the large family of about fifty low-$T$ unconventional heavy - fermion
superconductors and other families of unconventional superconductors with
higher $T_c$s, notably the doped Mott insulators of the cuprates, organic
charge-transfer salts and some of the Fe-based superconductors. Our study
suggests that heavy-fermion superconductivity near an AF QCP is a robust
phenomenon.
