Search built using Postgres is underrated. It can do a lot if used properly.
there are on different levels, a search on a sql database will have real time results, while on solr / elasticsearch it's going to have a delay (from milliseconds to minutes). That delay gives the advantage to build a series of data structures much more suited for search than the ones on a database.
I built several search systems for classified listing sites, something like solr is a life saver once you get enough traffic. Is much easier to scalate than a sql database, and you can do much more things. The easiest example is a facet, for example you make a search on a car listing site, and you want to show how many cars from each brand you are matching, with sql you have to make another query, while in solr you can get those results in the same query. Now, add the model, the color, the gas type, the transmission, the place, etc. that actually grows easily to something unescalable, while with solr you can do easily.