Here is a little research that explored RDBMS vs NoSQL using MySQL vs Mongo, the conclusions were inline with @Sean Reilly's response. In short, the benefit comes from the design, not some raw speed difference. Conclusion on page 35-36:
RDBMS vs NoSQL: Performance and Scaling Comparison
The project tested, analysed and compared the performance and scalability of the two database types. The experiments done included running different numbers and types of queries, some more complex than others, in order to analyse how the databases scaled with increased load. The most important factor in this case was the query type used as MongoDB could handle more complex queries faster due mainly to its simpler schema at the sacrifice of data duplication meaning that a NoSQL database may contain large amounts of data duplicates. Although a schema directly migrated from the RDBMS could be used this would eliminate the advantage of MongoDB’s underlying data representation of subdocuments which allowed the use of less queries towards the database as tables were combined. Despite the performance gain which MongoDB had over MySQL in these complex queries, when the benchmark modelled the MySQL query similarly to the MongoDB complex query by using nested SELECTs MySQL performed best although at higher numbers of connections the two behaved similarly. The last type of query benchmarked which was the complex query containing two JOINS and and a subquery showed the advantage MongoDB has over MySQL due to its use of subdocuments. This advantage comes at the cost of data duplication which causes an increase in the database size. If such queries are typical in an application then it is important to consider NoSQL databases as alternatives while taking in account the cost in storage and memory size resulting from the larger database size.