You've actually got an amazing choice, two of the best cities in Europe in my opinion. I live in one right now and have for 10 years. I am from the other country with lots of family there, regular visits and have also been to high school for a few months so I feel in a really good position to comment. Here are a few of my thoughts about it.
Funny how people who've been on holiday just say that Zurich is expensive and give the cost of a coffee etc. There's so much more to it than that! When you live in a place and are paid an equivalent good local salary, cost of bills, rent/mortgage, health insurance and TAX come into play. The different tax levels of these two countries are massively different and I think you should look into it. I think you could probably save more in Zurich if you are careful. Mortgages are so low, less than 2% that buying there seems a good option. But that might be after a while. You can also live in a place with particularly low taxes (though then cost of housing is more more).
If you are not in a rush to work, then Zurich might work well. Many more women/mums in DK work than in Switzerland, it's actually the norm and you may meet more mums in Zurich and also be more acceptable to stay at home. That said, plenty of mums in CH work but you just need to check the school offers more care (not all do).
There's something cool and fun about Copenhagen, love the dress sense of the scandinavians generally, but Zurich's not too bad either even though it's more conservative. I think you could have a great time in either; arts and cultural events are better in Copenhagen. It's more liberal and laid back in Copenhagen.
I love the way that Switzerland is so functional, like the public transport connections are timed so perfectly! It all has a certain smoothness to it. Everything works so well and is so clean and perfect that it seems surreal.
The weather in Zurich wins, swimming in the lakes in summer while looking at snow filled peaks is nothing short of magical. Imagine how good a skier your child will be, and you too! In an hour and a quarter you are in the mountains (even less!!). A lot of people have second homes in the mountains and ski every single weekend.
Both countries have great homes, are comfortable and warm etc.. with a high quality of workmanship. Denmark is more stylish with the interiors though!!
Both are quite racist countries, I find that the Danes can be quite outspoken about it, sometimes I am very shocked by what they openly admit to, without a thought. Danish people are generally friendlier and more fun if I had to generalise (loads of exceptions of course).
Schooling, both begin late, more like 7. Thereafter, Swiss schooling can be HARD, plenty of exams, tests and high standards, quite competitive, not like all the playing in forests in the early days! Seems a bit more child centre red in Denmark. It's possible to send your children to English lessons in reading and writing alongside local schooling. There are plenty of classes around Zurich, but not sure about Denmark, (I think not but could be wrong here).
It sounds like you have a tough choice, book mini breaks to both and see what you think. Do the salary calculations really carefully, there's loads of advice out there if you look.
What would I choose? As a single lady, or without kids, or if I were younger - Copenhagen - it's more interesting and fun. Now I have kids, it would be Zurich.
Great choice, good luck and let us know about the decision you come to.