Solr vs ElasticSearch - the million-dollar question. :-)
Broadly, Solr and ElasticSearch essentially have the same feature-set and address the same problem - that of building a fast, feature-rich search application on top of Apache Lucene.
Both provide (now standard) search features such as:
In fact, Solr and ElasticSearch are so similar, there is even an ES plugin that allows you to use Solr clients/tools with ElasticSearch!
For all practical purposes, there is no real reason to choose Solr over ElasticSearch or vice versa. Both have mature codebases, widespread deployment and are battle-proven. There are of course small variations in the two, such as ElasticSearch's percolation feature, and Solr's Pivot Facets.