  Star clusters (SCs) and active galactic nuclei (AGNs) are promising sites for
the occurrence of hierarchical black hole (BH) mergers. We use simple models to
compare hierarchical BH mergers in two of the dynamical formation channels. We
find that the primary mass distribution of hierarchical mergers in AGNs is
higher than that in SCs, with the peaks of $\sim$$50\,M_{\odot}$ and
$\sim$$13\,M_{\odot}$, respectively. The effective spin ($\chi_{\rm eff}$)
distribution of hierarchical mergers in SCs is symmetrical around zero as
expected and $\sim$$50\%$ of the mergers have $|\chi_{\rm eff}|>0.2$. The
distribution of $\chi_{\rm eff}$ in AGNs is narrow and prefers positive values
with the peak of $\chi_{\rm eff}\ge0.3$ due to the assistance of AGN disks. BH
hierarchical growth efficiency in AGNs, with at least $\sim$$30\%$ of mergers
being hierarchies, is much higher than the efficiency in SCs. Furthermore,
there are obvious differences in the mass ratios and effective precession
parameters of hierarchical mergers in SCs and AGNs. We argue that the majority
of the hierarchical merger candidates detected by LIGO-Virgo may originate from
the AGN channel as long as AGNs get half of the hierarchical merger rate.
