  La$_3$Co$_4$Sn$_{13}$ and La$_3$Ru$_4$Sn$_{13}$ were categorized as BCS
superconductors. In a plot of the critical field $H_{c2}$ vs $T$,
La$_3$Ru$_4$Sn$_{13}$ displays a second superconducting phase at the higher
critical temperature $T_c^{\star}$, characteristic of inhomogeneous
superconductors, while La$_3$Co$_4$Sn$_{13}$ shows bulk superconductivity below
$T_c$. We observe a decrease in critical temperatures with external pressure
and magnetic field for both compounds with $\frac{dT_c^{\star}}{dP} >
\frac{dT_c}{dP}$. The pressure dependences of $T_c$ are interpreted according
to the McMillan theory and understood to be a consequence of lattice
stiffening. The investigation of the superconducting state of
La$_3$Co$_x$Ru$_{4-x}$Sn$_{13}$ shows a $T_c^{\star}$ that is larger then $T_c$
for $x<4$. This unique and unexpected observation is discussed as a result of
the local disorder and/or the effect of chemical pressure when Ru atoms are
partially replaced by smaller Co atoms.
