Of course the looks should be the same, at least for non-Dwarves. Tolkien said so. Only Dwarf NPCs should have the ability to notice the differences. And yes, Dis was a stretch too far in my opinion.
Tolkien said they are very similar in appearance, however, no suggestion is ever made about them being very similar in personality, so I would expect some style differences with the way they let their hair/beards grow and the clothes that they wear. They probably should have the option to wear makeup as well.