I have a site-to-site VPN between two offices. Office A hosts a web service that Office B wants to access. The web service is accesible from the public internet (http://www.example.com) and on the internal network (http://webserver.domain.local).
Which interface's access going to be more efficient to use? Using the internal system looks quicker in a tracert because it's only two hops, but we all know that between the two VPN endpoints there's just as much routing going on as if I were using the public interface.
There's no pass-through authentication going on, so there's no advantage in NTLM or anything.