Stamford has the state’s second-largest Republican party. New Haven has not elected a Republican mayor since Truman was in the White House.

As the two cities’ elected leaders, Stamford Mayor Dan Malloy and New Haven Mayor John DeStefano Jr., face off for the Democratic Party’s gubernatorial nomination, the two candidates’ track records in their hometowns are becoming increasingly well-known, as are the differences between the two cities’ political and socioeconomic compositions — such as the absence since the 1950s of a viable New Haven Republican Party and the fact that New Haven’s poverty rate is nearly three times that of Stamford. As DeStefano travels the campaign trail, he has been emphasizing how much he has accomplished while also reminding his audiences that he leads a city much poorer than Stamford and whose reliance on tax-exempt institutions makes its governance particularly challenging.

“We’re proud of who we are as a city, but making New Haven work is a different kind of challenge than other cities,” DeStefano said in a debate against Malloy in Canton on Saturday.

According to the Connecticut Economic Resource Center, the median household income in New Haven is 50 percent that of the rest of the state, and a quarter of the city’s families live beneath the poverty line. In Stamford, the median household income is 110 percent the state’s average, and 8 percent of families are in poverty. The three biggest employers in Stamford are all corporations — Pitney Bowes, UBS Warburg and General Electric Capital Corporation — whereas New Haven’s three biggest employers are Yale University, Yale-New Haven Hospital and the Hospital of St. Raphael, all three of which are nonprofit, tax-exempt institutions.

“There’s definitely a difference between Stamford and New Haven, and you can’t draw too many comparisons between the two cities,” Ward 26 Alderman Sergio Rodriguez said.

Malloy’s campaign boasts that crime has decreased in seven of his eight years as mayor and that he has created citywide preschool, providing pre-kindergarten education to all 4-year-olds. DeStefano, on the other hand, has had to address a slight increase in the rate of violent crime and test scores on the Connecticut Mastery Test that are 50 percent lower than Stamford’s.

“Accomplishing reduced crime and increased access to pre-K is much more difficult in a city stands at 60 percent of national income,” DeStefano said after the debate. “Our successes are harder fought.”

During the debate, Malloy cast doubt on DeStefano’s ability to defeat Rell in November, arguing that the New Haven mayor has never faced credible Republican opposition, and he criticized the Elm City’s lackluster financial situation. Three months ago, a New York bond agency downgraded the city’s bond rating to A- because of the city’s heavy reliance on one-time revenue sources and its high level of debt.

“You’re the mayor this year, and your municipal bond rating was downgraded — that’s not the fault of the people who live in your community,” Malloy said. “We need to be ready to be held accountable for our actions, because the Republicans will.”

At the time of the downgrade, City Hall officials said the agency’s criticisms were already being addressed by the city’s financial officers. Concerning opposition candidates, DeStefano said he has faced challenging elections in Democratic primaries, most recently from state Sen. Martin Looney, a Democrat representing New Haven, in 2001.

DeStefano has drawn on his experience with Yale in formulating some of his policy proposals. In a proposal to improve job growth released in February, he suggested creating a $50 million statewide homebuyer program modeled after the Yale initiative that has helped more than 700 employees purchase homes in New Haven.

“I use the relationship with Yale as a model for what has to be done in other areas of the state,” he said, referring also to the need for each city to capitalize on its unique features. He suggested, for example, that Bridgeport could profit more from its deep-water port, one of few in the region.

In promoting the development of engineering and science-research jobs in the state, DeStefano has also pointed to his work with Yale and Science Park. According to the Office of Cooperative Research, Yale-affiliated entrepreneurs establish between three and five new companies in New Haven each year.

Despite the back and forth between Malloy and DeStefano about whose record is more impressive and who would be better able to attract Republican crossover vote, Democratic voters in the more suburban and rural towns say the fact that each mayor has successfully managed a major urban city is impressive in itself, regardless of the details of their respective records.

“I think the experience that they have there really prepares both of them for the governorships, because they do deal with a myriad of issues even though both cities are very different,” said Mary Tomolonius, first selectwoman of Canton.

Tomolonius added that there are some issues important to nonurban voters, such as the preservation of open space, which neither mayor has had to tackle seriously within his own city.