I analyze hundreds of GB of JSON log files from a custom analytics solution and I've found RedShift (essentially postgres) wonderful. The portions of the schema that are consistent I've reified into columns and the one misc data element I have on my objects I stick into a large varchar column that I query with Redshift's JSON functions. It wouldn't work if I had to do intense JSON queries, but I don't find myself needing to.
SQL has a very rich and mature query language as well. I can't imagine using MongoDB in nearly the capacity I use Redshift.
EDIT:
If you are currently using MongoDB and it works that's great. It wouldn't be the direction I would personally head in though if I were to start from scratch.
I have to second RedShift; it's been very easy to use, and just as importantly, it's dirt cheap to start out with. I used it to create a customer data warehouse for my current company; a mix of traditional flat data and JSON data that's either stored as large varchar columns or parsed into columns.
More to the data science part of it, it's allowed me to link together and analyze gigabytes of customer data. Easy Tableau plug-and-play integration was also a big selling point; it allowed me to give access to all the data to anyone who wanted it, without being bogged down by daily requests.
