  We provide a comprehensive comparison of a coupled channels calculation, the
asymptotic bound state model (ABM), and the multichannel quantum defect theory
(MQDT). Quantitative results for $^6$Li -$^{133}$Cs are presented and compared
to previously measured $^6$Li -$^{133}$Cs Feshbach resonances (FRs) [M. Repp et
al., Phys. Rev. A 87 010701(R) (2013)]. We demonstrate how the accuracy of the
ABM can be stepwise improved by including magnetic dipole-dipole interactions
and coupling to a non-dominant virtual state. We present a MQDT calculation,
where magnetic dipole-dipole and second order spin-orbit interactions are
included. A frame transformation formalism is introduced, which allows the
assignment of measured FRs with only three parameters. All three models achieve
a total rms error of < 1G on the observed FRs. We critically compare the
different models in view of the accuracy for the description of FRs and the
required input parameters for the calculations.
