Firebase's advantage is that it is a whole mobile platform, not a database. Crashlytics, Analytics, Cloud Messaging, Remote Config, A/B testing and App Distribution are all there, they all work, and they are all wired into the same project. If you are shipping an iOS and Android app, that bundle is worth more than any single technical property of the datastore.
Supabase's advantage is that it is Postgres. Relational modelling with real foreign keys, joins that don't require denormalising your entire schema, extensions, and a migration path off the platform that is a pg_dump rather than a rewrite.
The deciding question is usually your data shape, not your framework. Firestore is a document store that charges per document read, which pushes you toward denormalisation and duplicated data kept in sync by Cloud Functions. That is a reasonable model for feeds and chat and user profiles. It is a painful model for anything with many-to-many relationships, reporting, or a finance-shaped correctness requirement.
Our call for most new web products is Supabase, because most new web products have relational data and a team that already knows SQL. For mobile-first products where offline is a first-class requirement, Firebase's client SDKs remain the best in the business and Supabase has nothing that matches Firestore's offline persistence out of the box.
The second-order consideration is Google. Firebase is a Google product with everything that implies — excellent infrastructure, and a company with a track record of deprecating things. Supabase is open source, self-hostable, and much younger.