The verdict
If you send invoices to business clients who pay by bank transfer or iDEAL, I'd pick Moneybird and skip Stripe. Moneybird takes online payments itself, including iDEAL, QR code, direct debit and card. If you sell software or online products and want payments and subscriptions built into your product, I'd pick Stripe, with an accounting tool such as Moneybird behind it.
The question to ask is whether you need to take payments inside your own product or website. If not, you probably do not need Stripe yet. If so, you will still need books, and Stripe does not replace them. Check which connector links Stripe to Moneybird and who maintains it.