If the limitations of MongoDB's query facilities are getting you down, consider Couchbase. Couchbase supports JSON data natively, and has a very general query language called N1QL ("nickel"). If you know SQL, N1QL will seem very familiar.

http://www.couchbase.com/n1ql

I'm on the N1QL dev team and would be happy to answer any questions about the language.

Does anyone have a benchmark of how current Postgres does against current Mongo as a key-value store?

This article is "praywalled"

But it's webscale!