We tested exactly this. Our conversion rate was appreciably higher when keeping users on the page (using the Braintree Vault) when compared with Paypal or Googl

We tested exactly this. Our conversion rate was appreciably higher when keeping users on the page (using the Braintree Vault) when compared with Paypal or Google. It seems to me that users have already decided to trust us at the point of putting in credit card information, and sending them off-site required them to rethink it.