Supabase and Firebase are both backend-as-a-service platforms for auth, database, and storage. Supabase is known for an open-source, Postgres-based (relational, SQL) platform you can self-host. Firebase is known for Google's mature platform with battle-tested realtime and mobile SDKs, tightly integrated with Google Cloud. Neither is objectively "better." The right pick depends on what you're optimizing for.
Choose Supabase if you want a relational Postgres database and the option to self-host or avoid vendor lock-in. Choose Firebase if you need Firebase's mature mobile SDKs and deep Google Cloud integration.