Scoring a model is a difficult task because there are several metrics that describe different things about the model; therefore, to really know if it is a good model, it takes business domain knowledge with understanding on what data the model was trained with and the various scoring metrics.
A note to consider: Although clients often prefer the idea of a regression, they often like the easy comprehension that a confusion matrix provides, and therefore, they like a binary classifier. If this is ever the case, but the client is better served by a regression, it is not a hard task to run one model as a regression and one model as a binary classifier, using the same data with the exception of the target column. This would offer the ease of explanation in a binary classifier and the robustness of a regression.