Braintree has a major advantage over Stripe: their terms of service. Did you actually read through all the prohibited businesses[1] in Stripe's ToS? Most of them are common-sense bad, but some of the descriptions are very general, and there are 56 of them.
Are you sure your business isn't providing "personal computer technical support"? Offering any "extended warranties" with goods your business is selling? Maintaining "quasi-cash or stored value"? Or maybe one your web site's users posted "sexually-oriented or pornographic products or services"? Stripe prohibits accepting payments "in connection" with those things.