The verdict
If you are an EEA freelancer or small company tired of manual bookkeeping, pick GoDutch. It puts the account, the cards and the receipts in one place and feeds your accounting package.
If you are a developer or a small product team that wants Postgres without running it yourself, pick Neon. Branching lets you test migrations against real data and give each pull request its own database.
If you are a software business, you may need both. Do not treat them as alternatives. Start with the problem that costs you time today, which is either your books or your database.