Copenhagen or Paris which city on a European trip?

I would pick Copenhagen; I've been to both, but generally I prefer Fennoscandian countries/capitals over the rest of EU. It's just "my thing".

I have done both, but never on the same travel.

Paris is a big main city, good for a week, would be a shame to go for less than 3 full days.

Copenhagen is much smaller, you can spend a week there, but most people will see much of what there is to see in a few days. And in one full day you can get a decent impression.

So I would say Copenhagen for a short visit, Paris for a longer stop.

Paris. Big global city, a lot to see. And you can go to London by train quickly.