Unfortunately it seems you have completely misunderstood the nature of both SQL and MapReduce. MapReduce is a distributed computation engine. While it can be used in that way it was never meant to be a database system. BigTable is proof enough of that.

In general, SQL is the syntactical representation of relational algebra with some hacky additions for programmer convenience. Comparing just "SQL" to the MongoDB language model is misguided since you then break down to a question of algebraic expressivity and relational power.

I'm not going to try and build a proof here but we do know that a formal relational algebra system is equivalent to first-order logic. As far as MongoDB's relational language goes, one would probably have to make an argument that it is equivalent to either tuple or domain relational calculus, but I know of no theoretical work that has attempted this. If anyone has any more information to the theoretical expressiveness of the MongoDB relational system I would love to read it.