Even those use cases can sometimes be met by an RDBMS. Postgres can outperform Mongo as a key value, or json doc store. But Mongo is what many people think of for something like that.
Because as someone who has tried to update JSON documents (1M/s) in both PostgreSQL and MongoDB I would strongly disagree. MongoDB with WiredTiger was at least 10x faster per node and in terms of pure updates one of the fastest databases I've ever seen. And before the trolls yes I was fsyncing to disk.
It is workable, though, via combination of batching, ensuyring indexes on hot fields have appropriate fillfactor, and making sure Postgres can use heap-only tuples.
Here's my old SO question on this and a well-comprehensive answer that's still actual and could be helpful for some cases: http://stackoverflow.com/a/1663434/116546
But I am sure that there are use cases for which PostgreSQL is going to be much faster in particular single field lookups on unindexed fields across all records.
My point is that it's never black & white to say Database A is faster than Database B. It's always use case dependent.
Point being when someone says something is faster without providing verifiable numbers... it should not really be taken seriously
Hint: you probably can't, the reason why you store data is that you can read it (query it) later. MongoDB could be 10000x faster with inserts, still not a considerable solution for us because it fails with many of the other aspect of providing a great data access layer.