We present a comparison between three cluster models applied to data obtained by the Arcminute Microkelvin Imager radio interferometer system. The physical model (PM) parameterises a cluster in terms of its physical quantities to model the dark matter and baryonic components of the cluster using NFW and GNFW profiles respectively. The observational models (OM I and OM II) model only the gas content of the cluster. The two OMs vary only in the priors they use in Bayesian inference: OM I has a joint prior on angular radius $\theta$ and integrated Comptonisation $Y$, derived from simulations, while OM II uses separable priors on $\theta$ and $Y$ which are based on calculations of the physical model. For the comparison we consider a sample of $54$ clusters which are a subsample of the second Planck catalogue of Sunyaev-Zel'dovich sources. We first compare the $Y$ estimates of the three models, and find that the PM generally yields lower estimates relative to the OMs. We then compute the Earth Mover's Distance between the $\theta$ - $Y$ posterior distributions obtained from each model for each cluster, and find that the two models which are most discrepant are PM and OM I. Finally, we compare the Bayesian evidence values obtained from each model for each cluster. OM I generally provides the best fit to the data but not at a statistically significant level, according to the Jeffreys scale. The highest evidence ratio obtained is actually in favour of the PM over OM I.