Just using population density doesn't give the full picture. Copenhagen metro area has a population of 2 million, while Malmös metro area is around 700k

In practice this means that Copenhagens busiest train station (Nørreport) serves (in non-pandemic times) 165k passengers a day while Malmo Central Station serves 46k passengers daily. Which gives a much better picture of the kind of density that would make a virus spread easier

Blaming the mass transport system is an other theory being used to explain why the region of Stockholm has a much higher per capita deaths than other regions. Stockholm has the only subway in Sweden, and it is speculated that elderly care workers are heavy users of it in order to operate multiple care homes from a central organization using employees that goes from one home to the next. In almost every other city in Sweden they tend to go by car.

But this again points towards the kind of restrictions that would be effecting in reducing the number of deaths. Stopping the subway, get people that work with risk groups to not be in places where there is a high risk of infections. Malmö in comparison has significant less movement within the city and people use the mass transport system a lot less. In practice there are buses and taxi, and not much else. A common remark is that Malmö is actually 4 smaller cities of different social status with very little intermingling.

One effective restrictions that some nations like Finland did early was to lock down the capital and impose significant restrictions locally in those regions. Treating people different within a country based on where they live is very unpopular, but as a strategy to prevent deaths it seems like something Sweden should have done. Again, it is not restrictions for "visit restaurants, go shopping, attend gyms and send children under 16 to school" that seems to be relevant takeaway from the data.