I have worked on both and kind of fan of both.
But you need to understand when to use what and for what purpose.
I don't think It's a great idea to move all your database to DynamoDB, reason being querying is difficult except on primary and secondary keys, Indexing is limited and scanning in DynamoDB is painful.
I would go for a hybrid sort of DB, where extensive query-able data should be there is MongoDB, with all it's feature you would never feel constrained to provide enhancements or modifications.
DynamoDB is lightning fast (faster than MongoDB) so DynamoDB is often used as an alternative to sessions in scalable applications. DynamoDB best practices also suggests that if there are plenty of data which are less being used, move it to other table.
So suppose you have a articles or feeds. People are more likely to look for last week stuff or this month's stuff. chances are really rare for people to visit two year old data. For these purposes DynamoDB prefers to have data stored by month or years in different tables.
DynamoDB is seemlessly scalable, something you will have to do manually in MongoDB. however you would lose on performance of DynamoDB, if you don't understand about throughput partition and how scaling works behind the scene.
DynamoDB should be used where speed is critical, MongoDB on the other hand has too many hands and features, something DynamoDB lacks.
for example, you can have a replica set of MongoDB in such a way that one of the replica holds data instance of 8(or whatever) hours old. Really useful, if you messed up something big time in your DB and want to get the data as it is before.
That's my opinion though.