Both solve entirely different classes of problem. There are functional overlaps for small problem domains, but as your infrastructure tries to do more, you may find a need to run several distinct lightweight services backed by a variety of datastores serving focused requests.
Many of you have already seen Kovacs' comparison of nosql stores. Just throw a SQL DBMS into the decision matrix. Consider how several might work together.
http://kkovacs.eu/cassandra-vs-mongodb-vs-couchdb-vs-redis
Fowler's microservice post is a decent introduction to the microservice architecture, which is more or less what I'm describing.
http://martinfowler.com/articles/microservices.html
Granted, this probably isn't how to get the MVP out the door. But once you grow, this architecture can prevent the formation of monoliths of pain.