The Gamma‐ray Burst Monitor (GBM) onboard the Fermi spacecraft has observed many tens of sufficiently bright events, which are suitable for individual analysis. In our previous study, we fit individual, bright terrestrial gamma‐ray flashes (TGFs) with Relativistic Runaway Electron Avalanche (RREA) models for the first time. For relativistic‐feedback‐based models, the TGF‐producing electrons, which are seeded internally by a positive feedback effect, are usually accelerated in a large‐scale field with fully developed RREAs. Alternatively, lightning leader models may apply to either a large‐scale thunderstorm fields with fully developed RREAs or to inhomogeneous fields in front of lightning leaders where RREAs only develop partially. The predictions of the latter, inhomogeneous models for the TGF‐beaming geometry show some differences from estimations of the relativistic feedback models in homogeneous fields. In this work, we analyze a large sample of 66 bright Fermi GBM TGFs in the framework of lightning leader models, making comparisons with previous results from the homogeneous‐field RREA models. In most cases, the spectral analysis does not strongly favor one mechanism over the other, with 59% of the TGF events being best fit with the fully developed RREA mechanism, which corresponds to high‐potential leader models. The majority of the GBM‐measured TGFs can be best fit if the source altitude is below 15 km and 70% of events best fit by leader models cannot be satisfactorily modeled unless a tilted photon beam is used. For several spectrally soft TGFs, the tilted beam low‐potential leader model can best fit the data.