Creating informative priors from large datasets and roll out on smaller dataset

What is your ultimate goal here? It’s difficult to know how to approach things if you aren’t entirely sure what you’re hoping to accomplish. If you are confident that the small and large data sets “should exhibit the same characteristics”, it’s not clear to me why you are entertaining the idea of using different models for the two settings. And the idea of “informative priors” is a bit unclear. How informative? Informative based on what?