A number of shopping cart systems already offer Bitcoin as a payment method. Most of them convert their Bitcoins to dollars using Coinbase. Braintree is going to compete with Coinbase for that business.
Coinbase is the big loser here. They're about to be run over by a much bigger company.
Bitcoin/Coinbase is being built in to the Braintree infrastructure. This is the same infrastructure that paypal uses. Bitcoin is now in PayPal, but consumers can not use it yet. Paypal is not going to be competing with coinbase. Paypal is using coinbase to convert bitcoin to usd. Coinbase is without a doubt making a cut. Coinbase is also likely going to be bought by paypal if this goes well. There is no reason for paypal, as big as they are, to develop the infrastructure that coinbase already has.