On the face of it, it is much better to be looking for work in the U.S. than in Europe. U.S. unemployment in January, seasonally adjusted, fell to 6.6%. In the euro zone, the latest figures put unemployment at close to double that—12%.

That is in part due to the better economic performance of the U.S., which resumed growth in 2009 after a recession induced by the financial crash. The euro zone, meanwhile, languished in a sovereign-debt crisis.

Looking more closely, the picture is more nuanced. The unemployment figures flatter the U.S. labor market. That is because a major contributor to the fall in the U.S. unemployment rate has been the withdrawal of large numbers of Americans from the workforce. The number of people employed has expanded—though data suggest only in line with the working-age population. But the labor-force participation rate—the number of people both in work and seeking work as a percentage of the total population—has shrunk.

By contrast, this rate has stayed largely unchanged in the euro zone. “If the euro area had seen a drop in the labor-force participation rate proportional to the decline experienced by the U.S., its unemployment rate would be 9.5%, below where it was at the beginning of the sovereign-debt crisis,” wrote Thomas Klitgaard and Richard Peck, two economists at the Federal Reserve Bank of New York, in a blog post this month.

Some euro-zone policy makers suggest this is a sign that things are better than usually depicted in Europe. Klaus Regling, the chief of the euro zone’s bailout funds, said the higher labor participation shows that the euro zone’s “labor market functions much better than people seem to understand.”

Mr. Regling says it also suggests the social consequences are less dire in Europe than a direct comparison of unemployment rates would suggest. “Despite the unemployment, more people actually have a job and an income than in the U.S. as a percentage of the population,” he said in a recent interview. Because more people are working, “the situation is not as dramatic as people might think only looking at the unemployment rate.”

There is a lot of variation among nations in the euro zone and high-unemployment economies like Spain and Greece are still a source of anxiety to policy makers. But it is still worth unpacking the differences in the labor markets on each side of the Atlantic.

In the U.S., the sharp drop in unemployment has increased anxieties that the economy will soon reach full capacity and that the small available pool of unemployed workers will start to drive up wages, igniting inflation.

That hint of an overheating labor market is tempered by the falling participation rate in the labor market. Two other New York Fed economists, Samuel Kapon and Joseph Tracy, have pointed out employment as a percentage of the working-age population (E/P) fell more than 4% in the 2008-09 recession and hasn’t recovered since.

“In its failure to recover, the E/P ratio would seem to depict a much weaker labor market than indicated by the unemployment rate,” they say. One reason for that, though, is changing demographics of the labor force—people have gotten older and are no longer looking for work.

On the other side of the Atlantic, demographics is also at play, though it is increasing the number of people in work. The growing participation of women—and, in particular, women over the age of 45—in the workforce is the biggest factor shaping the labor market, suggest Messrs. Klitgaard and Peck. The trend for women over the age of 45 is evident in the three largest euro-zone economies: Germany, France and Italy. This is a cohort of women who, unlike their mothers, are accustomed to working and are now crossing the 45-year-old threshold.

This trend is likely to continue. Labor-force participation rates for women under 45 are roughly the same in the U.S. and the euro zone, at just under 70%. But in the euro zone, fewer than 40% of women over 45 are in the workforce—while the figure is close to 50% in the U.S. As more women enter the workforce, lowering the euro-zone unemployment rate will continue to be an uphill struggle.

Jean Pisani-Ferry, the head of policy planning in the French prime minister’s office and a former director of the Bruegel think tank, says pension reforms that have raised the retirement age have also helped expand the labor force.

But his view of the euro zone’s labor market is less positive than Mr. Regling’s. One worrying trend, Mr. Pisani-Ferry says, is the declining involvement of young people in the jobs market.

Another is what underlies the euro zone’s employment performance: very weak growth in productivity—a measure of the efficiency of economic output. While U.S. productivity grew 1.5% annually from 2008 to 2012, euro-zone productivity grew barely at all. If that sickly performance becomes entrenched, it will hurt economic growth for the long term.

Write to Stephen Fidler at stephen.fidler@wsj.com