I like Aarhus but I'm not sure what they say about it. I was born and raised here, then at 19 I moved to Aalborg. A few years later I changed university and moved to Odense (they are the 3rd and 4th largest cites). I've spent a lot of time in Copenhagen over the years, both for work and in my private life. I don't think there is too much difference between Odense or Aarhus, I didn't like Aalborg as much but it's been 20+ years since I lived there. What I miss most about Odense (aside from house prices) is that it's closer to Copenhagen, but my now wife lived in Aarhus when we met, and I found a job here easily so...
Anyway, I think the biggest difference is between Copenhagen and the rest of our cities. Copenhagen is different in that it has a lot more going on in terms of basically everything. I'm personally happy I'm not raising children in Copenhagen, mostly because of the cost of living.
We're just 5.5 million people though, so it's not like there is that much of a difference between places. When I say that I miss being closer to Copenhagen, we're talking 1,5 hours closer... It still only takes 3 hours from here.
If you work in IT like I do, Aarhus is a little more boring than both Copenhagen and Odense. Odense has a lot of IoT and robotics going on, and Copenhagen has everything. In the Aarhus area you'll probably want to work with C#, PHP, Java, Typescript or Python and Azure + general Microsoft products if you're going to work in tech.