It is a well-observed result that different nuclear input models sensitively affect Hauser-Feshbach (HF) cross-section calculations. Less well-known, however, are the effects on calculations originating from nonmodel aspects, such as experimental data truncation and transmission function energy binning, as well as code-dependent aspects, such as the definition of level-density matching energy and the inclusion of shell correction terms in the level-density parameter. To investigate these aspects, Maxwellian-averaged neutron capture cross sections (MACS) at 30 keV have been calculated using the well-established statistical Hauser-Feshbach model codes talys and non-smoker for approximately 340 nuclei. For the same nuclei, MACS predictions have also been obtained using two new HF codes, cigar and sapphire. Details of these two codes, which have been developed to contain an overlapping set of identically implemented nuclear physics input models, are presented. It is generally accepted that HF calculations are valid to within a factor of 3. It was found that this factor is dependent on both model and nonmodel details, such as the coarseness of the transmission function energy binning and data truncation, as well as variances in details regarding the implementation of level-density parameter, backshift, matching energy, and giant dipole strength function parameters.