When we originally deployed Phabricator, we started out using the Elasticsearch back-end for searching phabricator Tasks / Objects. Unfortunately, after launching with Elasticsearch there were quite a few user complaints about unexpected search behavior and we eventually made the (IMO, somewhat hasty) decision to switch to using the MySQL Full-text search backend.
Now that we reached the scalability limit of MyISAM fulltext search, we've been sort of forced to switch to Innodb Fulltext search (see T146673)... The fulltext search feature in innodb is not as mature as MyISAM fulltext. The ranking algorithm is very simplistic and I expect results to be lower quality than before.
ElasticSearch should be far superior to mysql for implementing phabricator search. Lets try again to solve the problems with phabricator's elasticsearch integration rather than settling for a much worse search experience in Innodb.
A bit of history
There is quite a bit of history behind Phabricator's search implementation. Some of the more relevant tasks I was able to dig up are linked below: