Other than that, API + custom UI seems better since you're paying for the usage instead of competing with other flat-fee users for what seem to be overprovisioned resources (claude.ai was always throwing https 500 or 'sorry we're too busy' errors for me until I switched to API).
Not sure if it's cheaper though - I never checked.
It's insane how bad the first party chat apps are though. That's reason enough to use the API.