Up to now, the excited charmed and bottom baryon states are still not well studied both experimentally and theoretically. In the present paper, we predict the mass of $Omega_b^*$, the only $L = 0$ baryon state which has not been observed, to be 6069.2 MeV. The spectra of charmed and bottom baryons with the orbital angular momentum $L = 1$ are studied in two popular constituent quark models, the Goldstone boson exchange (GBE) and the one gluon exchange (OGE) hyperfine interaction models, respectively. Inserting the latest experimental data from the Review of Particle Physics, we find that in the GBE model, there exist some multiplets ($Sigma_{c(b)}$, $Xi_{c(b)}$ and $Omega_{c(b)}$) which total spins of three quarks in their lowest energy states are 3/2, but in the OGE model there is no such phenomenon. This is the most important difference between the GBE and OGE models. These results can be tested in the near future. We suggest more efforts to study the excited charmed and bottom baryons both theoretically and experimentally, not only for the abundance of baryon spectra, but also for determining which hyperfine interaction model is realized in nature.
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