Bear in mind, I've only experimented with MongoDB...
From what I've read, DynamoDB has come a long way in terms of features. It used to be a super-basic key-value store with extremely limited storage and querying capabilities. It has since grown, now supporting bigger document sizes + JSON support and global secondary indices. The gap between what DynamoDB and MongoDB offers in terms of features grows smaller with every month. The new features of DynamoDB are expanded on here.
Much of the MongoDB vs. DynamoDB comparisons are out of date due to the recent addition of DynamoDB features. However, this post offers some other convincing points to choose DynamoDB, namely that it's simple, low maintenance, and often low cost. Another discussion here of database choices was interesting to read, though slightly old.
My takeaway: if you're doing serious database queries or working in languages not supported by DynamoDB, use MongoDB. Otherwise, stick with DynamoDB.