Exchange 2010 and 2013 coexistance

In Microsoft's Proffered architecture, it says to move dns to point to exchange 2013 once it is ready in exchange 2010 coexistence environment. I have a question here.

- If we don't change URL to point to 2013 CAS and setup different URL for it and just migrate mailboxes from 2010 to 2013 which will pick up to new URLs with OA?

-Also i was checking deployment assistant it says to use or can be used same URL for all services, however i have heared some where else that OA internal and external URL should be different because of authentication issue. 

Any advise?

Thanks

SMF