I could be wrong but I believe Dwolla is a totally new payment system that actually bypasses the credit card system by directly depositing/debiting bank accounts. It designed to replace credit cards and requires the customer to signup for a Dwolla account to pay[1]. Stripe on the other hand is just an API for processing credit cards.

[1] http://www.businessinsider.com/this-28-year-old-is-making-su...