Comparing probability scores from logistic models


I want to be able to compare the probability scores from 2 different logistic regression models. I think it is not appropriate to directly compare them since they represent different equations.

1. It is valid to compare them using any normalization approach? If so, will the following approach work?

2 steps:
a. Applying same scale to 2 probability scores e.g. scaled score = a +[ b/ln(2)]*[probability score - ln(c)]
b. Normal standardization: z - score = (scaled score - mean)/Std dev

2. Is there any better approach?

help is appreciated!