Elasticsearch is massively more powerful and flexible.

The way I'm doing aggregation counts on top of PostgreSQL is very unlikely to scale to millions of documents. Elasticsearch pretty much acts as a real-time, horizontally scalable map/reduce engine so expensive aggregations get executed on multiple shards and the results are gathered back together.

You may find my talk from DjangoCon this year interesting: https://speakerdeck.com/simon/the-denormalized-query-engine-... / https://www.youtube.com/watch?v=NzcvewgqYog