Butkovitz, who was a state House member when he was first elected controller in 2005, derides Mandel as an irresponsible proponent of tax policies that will hurt city residents and help big-business interests.
Mandel, 44, a self-described "budget bulldog," says Butkovitz has not done the work required of a City Controller, including regular audits of city agencies.
He also accuses Butkovitz of seeking re-election while planning a run for mayor in 2015.
Butkovitz has said he is still considering the race for mayor.
Mandel, who worked for former City Controller Jonathan Saidel, finished third in the 2009 Democratic primary for the post.
Zecca, 60, who served as an attorney in the city's Law Department for 20 years, says Butkovitz is irrelevant, ignored by those he is supposed to keep an eye on.
He slams Mandel for filing a lawsuit to push the city into implementing the Actual Value Initiative, which will change the way the city taxes property.
Butkovitz and Mandel have fought this campaign primarily with literature mailed to voters.
Mandel briefly ran a television commercial on cable, prompting a backlash from some self-described "progressives" who thought the ad unfairly blamed Butkovitz for the school district's budget crisis.
Zecca, an inexperienced but enthusiastic politician, loaned his campaign more than $67,000 this year while rasing a scant $7,975 from 16 contributors, according to a campaign-finance report filed last week. Zecca still had more than $75,000 in his fund as of May 6.
The city controller runs in what is often referred to as an "off-year" election because there are few races on the ballot that draw widespread public interest.
That gives considerable sway to established party officials, who drive to the polls what few voters turn out. That would seem to give an edge to Butkovitz, a ward leader with strong support from his party.
Mandel is seeking to build a grassroots coalition of voters unhappy with Butkovitz's performance while Zecca pitches himself as an alternative option.
Incumbent District Attorney Seth Williams and Republican Danny Alvarez face no primary challengers on Tuesday.
Terry Tracy, the Republican candidate for city controller, is also unopposed in the primary.
On Twitter: @ChrisBrennanDN