2.4 introduced text indexes for full text search as a beta, and 2.6 finishes the job of fully integrating them into the product - they are fully supported with the new release (including in the aggregation framework).

In terms of how they compare, I'm not familiar enough with Elasticsearch to comment, but for basic test searching needs, the implementation in MongoDB is pretty decent. More here:

http://docs.mongodb.org/manual/core/index-text/#text-search