Apart from the "Remember me anywhere"-feature (which I wasn't aware of, is this a recent addition?), I think Stripe and Braintree.js are recognized by users as

Apart from the "Remember me anywhere"-feature (which I wasn't aware of, is this a recent addition?), I think Stripe and Braintree.js are recognized by users as yet another credit card form, and not as a virtual bank with a private login the way PayPal is. Most users probably don't even notice they're not handing their CC info to the website, but to some third-party service instead. So they'd have to be comfortable with giving their payment details to the shop anyway. If I chose PayPal however, which is marketed as a safe way to pay online, I don't want to have to put any trust in the site itself. That's why I want to be able to verify I'm actually entering my login details on PayPal's site.