I've been to both and loved both. We stayed in a Radisson in Copenhagen, there are 2, can't remember which one it was. Public areas were nice, rooms tiny and dated.
Copenhagen is beautiful and SO clean but it's the most expensive place I've ever been and we travel lots. Lunch in a little cafe (2 cokes, fish & chips, a club sandwich and a coffe) €65! Taxis are very pricey too. We didn't eat in touristy places but even so I was amazed at how expensive it was. Our Danish friends are the only people who visit us who think Dublin is cheap.
Edinburgh is a lovely city. Can highly recommend the Radisson there. The city has great bars and restaurants, had an amazing Thai meal there, wow.
Given the choice I'd prefer Edinburgh. Marginally!