In a case with two EPiServer installations, one public outside the firewall without Admin interface and one inside the firewall with Admin interface.
What is best practice for setting up the server domain names with this infrastructure?

I can see advantages with using the same domain name (ex www.foobar.com) both inside and outside the firewalls,
and instead letting the internal dns point to the internal server when inside the firewalls.

I can also see advantages with using different domain names (ex  internal.foobar.com for inside and www.foobar.com for outside). 

Suggestions?