I have "Copenhagen" tattooed on the inside of lip. What's better; laser treatment or surgical excision?

If the tattoo is small, excision could work.  There is a lot of redundancy in the mucosa (skin) of the inner lip.  Often some of it can be removed and everything would look normal with minimal scar.

I would advise against having this area excised. Even though it may be a little cheaper overall, the pain and downtime afterward would be substantial. Your best bet, based on what is currently available for the treatment of tattoos, is to have it treated with a laser such as the PicoSure. It is a little more expensive per treatment than older tattoo laser devices, but you would require less sessions to completely remove it. If the tattoo is black, I would estimate 4-8 sessions (more sessions for the bolder lettering) would be enough.