For your consideration I'm submitting you a research I made together with my colleague Wouter.
We compared the 2 databases for our specific use case on medical data stored using FHIR standard.
This is indeed a very restrictive use case, and moreover under read only circumstances. We are aware of that.
We might consider in a near future to enlarge the scope of the research including read and write operations, more use cases, using partitioning, and/or scaling Mongo.
This has to be considered as a starting point and we would like to share our results aiming in constructive feedbacks and perhaps fix mistakes or inaccuracies you might find.