Dont get me wrong. I think Edinburgh is beautiful. I have good memories of visiting Edinburgh when i was still quite young and I remember how excited I was to go to the castle. I used to really love going to castles, cathedrals and other sites like that and Edinburgh castle was great. I also have fond memories of Edinburgh zoo. How amazing is that place? I like Edinburgh for many of the same reasons i love Durham and Melbourne, in my experience, didnt have any of the same qualities. It is, as you say, a very different place. Melbourne was just outstanding though.
Oh and incase you dont know Durham, here you go.
DURHAM CATHEDRAL
DURHAM CASTLE