  We apply the general formalism derived in N. Penalva et al. [Phys. Rev. D
101, 113004 (2020)] to the semileptonic decay of pseudoscalar mesons containing
a $b$ quark. While present $B\to D^{(*)}$ data give the strongest evidence in
favor of lepton flavor universality violation, the observables that are
normally considered are not able to distinguish between different new physics
(NP) scenarios. In the above reference we discussed the relevant role that the
various contributions to the double differential decay widths
$d^2\Gamma/(d\omega d\cos\theta_\ell)$ and $d^2\Gamma/(d\omega dE_\ell)$ could
play to this end. Here $\omega$ is the product of the two hadron
four-velocities, $\theta_\ell$ is the angle made by the final lepton and final
hadron three-momenta in the center of mass of the final two-lepton system, and
$E_\ell$ is the final charged lepton energy in the laboratory system. The
formalism was applied there to the analysis of the $\Lambda_b\to\Lambda_c$
semileptonic decay showing the new observables were able to tell apart
different NP scenarios. Here we analyze the $\bar B_c\to \eta_c
\tau\bar\nu_\tau$, $\bar B_c\to J/\psi\tau\bar\nu_\tau$, $\bar B\to
D\tau\bar\nu_\tau$ and $\bar B\to D^*\tau\bar\nu_\tau$ semileptonic decays. We
show that, as a general rule, the $\bar B_c \to J/\psi$ observables, even
including $\tau$ polarization, are less optimal for distinguishing between NP
scenarios than those obtained from $\bar B_c \to \eta_c$ decays, or those
presented in N. Penalva et al. for the related $\Lambda_b \to \Lambda_c$
semileptonic decay. Finally, we show that $\bar B\to D$ and $\bar B_c\to
\eta_c$, and $\bar B\to D^*$ and $\bar B_c\to J/\psi$ decay observables exhibit
similar behaviors.
