If anything, using Braintree removed all sorts of restrictions. They keep all the credit card information. Let them worry about PCI Compliance, not me.
If PayPal really enhanced customer trust, I'd expect to see more large retail corporations using it as a payment option.
There's a whole class of people who can't get a credit card in the first place, but they can use paypal tied to their bank and move money in.
Paypal is more universal around the world than most other cards. Someone may have a JCB card or a Switch card - my standard merchant account gives me a harder time with those, and charges me a heftier fee, and in some cases I can't take 'overseas'-based cards at all (Solo cards, for example) - but those people in those countries can use PayPal - and they do with me.