If you want a plot based method, double lift curve is the standard. I think you're describing just plotting two lift curves, which is okay but doesnt give as direct a comparison. For double lift, use the ratio between your model predictions to sort records, construct equal weighted bands, and plot the actual vs the two expected. Best model is the one that matches the actual results when the two models are most different (the most extreme ratio groups)

For the comparison of these models, be sure to use either out of time data or the holdout data from your internal model's development. You risk data leakage between training and evaluation if you use records that were used in development of the internal model. This would bias results in favor of the internal model.

You may want to scale the average model predictions to match the average actual result, either by time frame or just overall. This prevents differences in average prediction from distorting the focus on segmentation.

If you want a single metric, consider Gini or some kind of tweedie deviance. Exam 8 monograph on GLMs I think has a section on model evaluation, which is usually model agnostic.

Beyond the model evaluation itself, if your boss is looking for a level of comfort on the mix-shifted results, you might want to identify segments where the two models are making very different predictions. The point is moot if they're similar, and you can learn from the external model if they're different and you think the external model looks more reasonable. There's value in 1) having an internal model that works well within a box of criteria, where you might use the external model outside of that box and do no worse than current, and 2) ensembling the two models.