Square transaction fees are deliberately simple: 1.75% for all card reader payments regardless of the type of card and where it is from, and 2.5% for all keyed-in payments regardless of whether the merchant or customer entered their card details remotely or in person.
With Stripe, you can save money if the majority of payments are made with European cards because those transactions cost just 1.4% + 20p. Non-European cards cost more than Square, though: 2.9% + 20p per transaction. The fixed 20p fee could in any case get expensive if most transaction amounts are low (20p of £5 is the equivalent of a 4% fee!). In addition, Stripe charges a 2% currency conversion fee on transactions paid in a different currency from the customer’s card.
With billing, Stripe merchants pay the same transaction fees for one-off invoices as through ecommerce (1.4% + 20 for European/2.9% + 20p for non-European cards), but automatically charging customers on a recurring basis costs only 0.5% per payment.
Payouts are free on both platforms, but Square gives the option to settle transactions instantly in your bank account for an extra 1% added to transactions.
PCI compliance (card security paperwork) is managed free of charge by Square, while Stripe encourages their users to address this but with some support provided. This could cost extra depending on the level of protocols required for your business. Chargebacks cost £15 each with Stripe, but are free with Square.