Hi - I'm living in London right now and from Australia.
Mostly what stands out about Copenhagen is the ridiculously extensive cycling infrastructure. Dedicated lanes, signage, signalling, parking...it's amazing. Also the entire culture is about the bike. People looked at me like I was a bit crazy when I didn't (yet) have a bike to get from one venue to another.
Cycling in Australian cities is nothing like it. It would also be impossible to implement it to the same extent in London.
The public transport is also excellent, the education opportunities and nice, open spaces. :)