One is document-oriented database software while the other is a fully-managed document-oriented database-as-a-service, so not at all a useful comparison.

MongoDB offers a fully-managed database-as-a-service as well (Atlas), for what it's worth.

I swa a talk once from one of the facebook game companies who simply stored the player state in a file. There is nothing more simple! They simply loaded the files content into the memory as long as the player was playing and then serialized to file