The big problem with all the off-the-shelf search solutions (RDBMS full-text search, ES, Algolia) is that search ranking is a complicated and subtle problem, and frequently depends on signals that are not in the document itself. Google's big insight is that how other people talk about a website is more important than how the website talks about itself, and its ranking algorithm weights accordingly.
ES has the basic building blocks to construct such a ranking algorithm. In terms of fundamental infrastructure I found ES to be just as good as Google, and better in some ways. But its out-of-the-box ranking function sucks. Expect to put a domain expert just on search ranking and evaluation to get decent results, and they're going to have to delve pretty deeply into advanced features of ES to get there.
AFAICT Postgres search only lets you tweak the ranking algorithm by assigning different weights to fields, assuming that the final document score is a linear combination of individual fields. This is usually not what you want - it's pretty common to have non-linear terms from different signals.