If Postgres works for you then great, but it doesn't really compare to Solr/Elasticsearch. I haven't used Algolia so I cannot comment on it. Postgres is hard to use beyond very basic keyword searching and it doesn't support many standard features such as phrase search.
Interestingly, Solr also can do a lot of database type work. It can store not just documents for text searches, but also for numeric fields, aggregations, pivoting, etc. A nice tool for a data analysis back end. Even the Hue project uses it for its dashboard maker.
