AFAIK, PostgreSQL doesn't provide a way to get the IDF of a term, which makes its ranking function pretty limited. tf-idf (and its varians, like Okapi BM25) are kinda table stakes for an information retrieval system IMO.
I'm not saying PostgreSQL's functionality is useless, but if you need ranking based on the relative frequency of a term in a corpus, then I don't believe PostgreSQL can handle that unless something has changed in the last few years. Usually the reason to use something like Lucene or Tantivy is precisely for its ranking support that incorporates inverse document frequency.
