  We present a unified model to describe the dynamics of optical frequency
combs (OFCs) in quantum cascade lasers (QCLs), incorporating both ring and
Fabry-P\'erot (FP) cavity configurations. The model derives a modified complex
Ginzburg-Landau equation (CGLE), leveraging an order parameter approach and is
capable of capturing the dynamics of both configurations, thus enabling a
comparative analysis. In the modified CGLE, a nonlinear integral term appears
which is associated with the coupling between counterpropagating fields in the
FP cavity and whose suppression yields the ring model, which is known to be
properly described by a conventional CGLE. We show that this crucial term holds
a key role in inhibiting the formation of harmonic frequency combs (HFCs),
associated to multi-peaked localized structures, due to its anti-patterning
effect. We provide in support a comprehensive campaign of numerical
simulations, in which we observe a higher occurrence of HFCs in the ring
configuration compared to the FP case. Furthermore, the simulations demonstrate
the model's capability to reproduce experimental observations, including the
coexistence of amplitude and frequency modulation, linear chirp, and typical
dynamic scenarios observed in QCLs. Finally, we perform a linear stability
analysis of the single-mode solution for the ring case, confirming its
consistency with numerical simulations and highlighting its predictive power
regarding the formation of harmonic combs.
