"Currently Azure Search does not offer configurable analysis modes" ( source: http://msdn.microsoft.com/en-us/library/azure/dn798920.aspx )

The configurable analysis is the cornerstone of the search functionality and is a huge portion of Apache Lucene (and therefore both Solr and ElasticSearch).

So, in my eyes, this offering has not outgrown the pure web-search domain yet.

(edit) Which is strange, because in another comment they do say they use ElasticSeach under the covers. I even thought that the API interface looked somewhat similar to ES.