Wave is genuinely free, and for invoicing-first businesses that's a real draw — it makes its money on payment processing, not the software. But the bookkeeping is still yours to do. Felix is a paid tool with a different job: it does the categorizing and reconciling for you and keeps your taxes ready year-round. Wave is a free ledger you keep; Felix is a bookkeeper you don't have to be.
Wave monetizes your payments and leaves the books to you. Felix does the books and charges for that directly.
If free-and-you-do-it works for you, Wave is a solid choice. If you'd rather the books just be done and tax-ready, that's what Felix is for.