You can comfortably do Bayesian model comparison here; have priors for µcon, µamn, and µsim, and let µpat be either µamn (under hypothesis Hamn) or µsim (under hypothesis Hsim), and let Hamn and Hsim be mutually exclusive. Then integrating out µcon, µamn, and µsim, you get a marginal odds-ratio for Hamn vs Hsim, which tells you how to update.

The standard frequentist method being discussed is nested hypothesis testing, where you want to test null hypothesis H0 with alternative hypothesis H1, and H0 is supposed to be nested inside H1. For instance you could easily test null hypothesis µcon >= µamn >= µpat = µsim against µcon >= µamn >= µpat >= µsim. However, for testing non-nested hypotheses, the methodology is weaker, or at least less standard.