the BESS model in MATPOWER/MOST is pretty comprehensive. you can set different values for BESS charging efficiency, and discharging efficiency. I recall there was even the option of modelling energy leakage (when the battery is not used). you can model the BESS degradation as a cost parameter in the BESS.gencost field.
the only downside is that you can't use any of the advanced models of BESS degradation (because MOST does not allow non-linearity in the model).