It looks like searchify is a hosted search solution, whereas Solr and ElasticSearch are distributions of search servers that can be deployed on your own hardware.
Technically Searchify is based on the open-sourced code from the previously proprietary IndexTank. So in theory you can run your own: https://github.com/linkedin/indextank-engine.
I'm skeptical about claims of different quality of relevancy results, since IndexTank/Searchify is also based on Lucene (looks like 3.0.1 in the canonical repo), and should share all the same fundamental relevancy and scoring functionality.
