Ambiguous URLs and their effect on Exchange 2010 to Exchange 2013 Migrations

I am in the process of transition from Exchange 2007 to 2013, OA is enabled on both Exchange 2013 and 2007 as well, should i configure the OA internal as NTLM and external as bsic authenticaation in both exchange servers. our domain name is contoso.local and externally we are registered with contoso.com. do you recommend to have internal and external url same in exchange 2013 for outlook any where like mail.contoso.com or should i use different internal and external url.

if i will enable ntlm for internal and basic for external and if outlook is configured to use basic then what will happen

Thanks