I looked into both of these companies last year and made the following observations back then:
Braintree looks great, but you need a rather large minimum monthly to sign with them (6 figures, can't remember the cutoff then). But they seemed to be the class act at the time.
Authorize.net just does not inspire trust, from their business practices to their flaky infrastructure (plus they've been a major target for attacks). They do have some pretty neat public APIs you can use.
Braintree looks great, but you need a rather large minimum monthly to sign with them (6 figures, can't remember the cutoff then). But they seemed to be the class act at the time.
Authorize.net just does not inspire trust, from their business practices to their flaky infrastructure (plus they've been a major target for attacks). They do have some pretty neat public APIs you can use.
Good luck! This is not an easy area.