I see several responses that mention MongoDB for purposes of comparison and seem to conclude Elasticsearch fares favorably.
It should be noted:
[1] Unlike MongoDB (which is a ground-up build), Elasticsearch is basically an API layer on top of Apache Lucene. This is relevant because they haven't built and don't maintain, control, or own the source of their primary IP.
[2] Unlike MongoDB (General Purpose) Elasticsearch is a single purpose database and good at/used for one thing and one thing only. It searches text fields for text.
So its potential use cases and thus marketshare is far more limited.