I don't understand why you would consider using Braintree in Europe (or anywhere) vs. going to Adyen directly.

The Adyen guys are smart, their technical platform is simple and robust, and unlike the Stripe/Square/Braintree guys, Adyen actually does the processing so they can offer better rates and are suitable for huge volume.

About the only downside is that "At-jien"'s b2b marketing is pretty terrible. They have some faux Apple videos on their site which I think undermines their technical sophistication.