We have a lot of in house expertise in ElasticSearch and choose it for a few reasons: 1) It's easier than Lucence/Sphinx to setup. 2) It's clustering support works out of the box and is so easy to configure it's not funny.
ES is basically a usability wrapper around Lucene. I've heard that Sphinx is better for a single node configuration, it's faster and uses less resources, but clustering with Sphinx is apparently tricky.
The other competitor, which I have no experience with is Solr, but this write-up http://karussell.wordpress.com/2011/05/12/elasticsearch-vs-s... gives an overview of the ES advantages over Solr.
I'm not a Full-Text Search expert, but a number of really smart people at my company evaluated a number of them for one of the most critical pieces of our production site and they chose ElasticSearch.