They have a similar public trust in government, similar social structures, demographics, and health systems, but wildly different coronavirus strategies.
Denmark locked down hard and early, shutting schools, borders, cafés, restaurants and shops. Sweden has taken a light-touch approach, shutting none of these things, and instead relying on the public's "common sense behaviour".
Last Wednesday, the two countries' health agencies both published their report cards, giving estimates on what difference their contrasting approaches had made to the rate at which the infection is spreading - the famous 'R number'.
The result? Not that much.
If the R number is 1, it means that each person infected goes on to infect an average of one other person during the course of their illness. So long as a country keeps R below one, the number of infections will steadily decrease until the pandemic comes to an end.
The Public Health Institute of Sweden estimated that Sweden's R number has fallen from 1.4 at the start of April to 0.85 at the end of April.
Denmark's SSI infectious diseases agency, meanwhile, estimated that Denmark's had fallen from about 1 at the start of April to about 0.9 at the end of April.
On the face of it, it looks like Sweden - without ever imposing a lockdown - has done a slightly better job at slowing the rate of spread.
Uno Wennergren, a mathematician and pandemic modeller at Linköping University, suspects Sweden's low number in part comes from growing levels of immunity in Stockholm, where the outbreak has so far been concentrated, and in part from social distancing.
"It looks like its a combination of herd immunity effect and lower infectability. Both seem to be acting simultaneously," he said.
If Swedes hadn't changed their behaviour on the recommendation of the Public Health Institute, he stressed, Imperial would have been proven right.
"We should always in the back of our mind remember what would happen if we went back to what we were doing in January or February," he said. "If we went back to that, it would not be nice."
So did Danes endure their long, strange month of home-schooling, home-working and zero social life for nothing? Not quite.
Denmark's much heavier lockdown helped push the R number as low as 0.6 in mid-April, only creeping back to 0.9 after it opened schools on April 15 - although the increase may have more to do with the weather and the effects of lockdown fatigue.
Sweden, on the other hand, saw an early and sudden peak in mid-March, when the infection rate briefly spiked above 3, and then a steady slow decline through April, with the rate only falling consistently below one after April 19.
This apparently small difference has had a big impact in terms of hospital admissions and death: Sweden's cumulative coronavirus death rate, at 274 deaths per million inhabitants, is now triple that of Denmark.
But as Sweden's Public Health Institute has maintained from the start, coronavirus will be with us for much longer than the month or so a country can reasonably maintain a full lockdown.
Sweden's state epidemiologist Anders Tegnell now estimates that as many as a quarter of people in Stockholm might already be immune. The capital might have herd immunity within weeks, he argues.
This doesn't say anything about the rest of Sweden. Wennergren warns that the sub-1 R number for Sweden as a whole might be heavily weighed down by a high immunity in Stockholm, masking a rapid spread elsewhere.
"We could end up on the other side of the Stockholm peak and think we’re doing fine, and instead get a wave-like plateau that is a result of different regions overlapping one another," he said. "What we are trying to do now is to model it by the different regions... Until we have done that, I think it will be really hard to know where this is going to land."
At the end of April, Wennergren estimated on Swedish national TV that between 10,000 and 20,000 people will ultimately die of coronavirus in the country. This means the virus has so far claimed, at best, only a quarter of its likely victims.
Denmark, on the other hand, faces the same dilemma as other locked down countries. Even with cafés, restaurants and most shops still shut, it has seen the R number creep up to 0.9.
How much more can it relax before it starts to see a second wave? And how much will its impressive success in curtailing the number of deaths last month affect its final death toll?
Clarification: An earlier version of this article said Imperial College researchers predicted that Sweden's approach would leave it with an R of above 3, leading to 40,000 coronavirus deaths by May 1. Imperial researchers did not estimate death figures. Instead, Paul Franks, a professor of epidemiology at Lund University, made calculations on fatalities. This paragraph has been removed and we apologise for the earlier confusion.