Having used all 3, Postgres search is my go to for most use case simply because I don't have to deal with managing deltas to an outside system and keeping things in sync. The search features are powerful and fast and PG's ability to combine multiple indexes in search results make it trivially easy to include a bit of full text search in a query right next to geographic distance filters or other conditions. You can also combine multiple types of searches on the fly if you're feeling whimsical.

IMO, the only time to reach for an outside system is when the data isn't being written to PG first (like log ingestion with elastic search) or when search is such a central part of your app that it mandates a separate dedicated system.