Will have an impact also in terms of economies of scale. Their transaction fees _should_ go down as they process a larger number of transactions. Makes the partnership much more strategic, and it makes sense why Starbucks also invested - might have been part of the package.
I'm having a hard time seeing how Starbucks has higher processing costs than Square. I think that Starbucks will continue to pay their low costs and be able to use Square as their platform. No reason Square couldn't process Starbucks transactions, too without needing to change their merchant accounts.