It’s an off election year in San Francisco, and the campaign for the sole open seat on the Board of Supervisors has yet to capture much attention beyond City Hall insiders.

But there’s a lot at stake.

The outcome of the Nov. 5 election will not only influence the political makeup of the board, it will also determine whether Mayor London Breed will have another ally — or another adversary — in City Hall. That means this campaign, which covers just one section of the city, could have a broad impact on San Francisco over the next four years.

Still, ask City Hall insiders who they think will win the District Five seat, and many will shrug. Because with one month to go, observers say the race is still neck and neck.

The Chronicle sat down with the two major candidates in the race to learn about their priorities. Supervisor Vallie Brown is a longtime friend of the mayor who appointed her to the seat last year, while tenants’ rights activist Dean Preston challenged Breed for her District Five seat in 2016 — only to lose by a tiny fraction of votes.

Like most elected leaders in San Francisco, both candidates say they want to increase affordable housing, address the city’s twin crises of homelessness and mental health, and improve public transportation.

But it’s in how they would approach these goals — and who their allies are — that their differences show.

Vallie Brown: She has a personal story to go along with many of the issues facing San Francisco: She knows what it’s like to have to live out of an RV. When Brown was a teenager, her mother died because she didn’t have proper health care. As an adult artist living in the city, she was evicted not once — but three times.

So when it comes to addressing homelessness, mental health care and affordability, Brown says she empathizes with what city residents are going through.

But her aptitude for the supervisor job, she says, comes from years as an activist and then a legislative aide at City Hall, where she learned how San Francisco’s lumbering political apparatus works. She believes that real change takes patience, strategy and a good relationship with the mayor.

Her critics, on the other hand, argue that her City Hall experience and long relationship with Breed are her greatest weakness. Her opponent, Dean Preston, who is running to her left, maintains the city needs dramatic, sweeping change — not the incrementalism that he says Brown represents.

The supervisor pushes back on the incrementalist label: “Saying you’re going to solve anything in one broad stroke is just not the way it is.”

Brown began as a neighborhood activist, who “was rattling the chains of City Hall” so much that she said then-Supervisor Ross Mirkarimi told her to work in his office to see how hard it is to get things done. Today, after years in City Hall, Brown casts herself as a pragmatist with activist flair.

“Vallie Brown’s campaign is more about ... trying to make change with her experience within the government, rather than as an outsider,” said Jason McDaniel, a political science professor at San Francisco State University. “It is a thin line to walk between saying ‘I want change, but I want to be realistic’ — because that can sound uninspiring.”

Her notable legislation that passed includes a plan to streamline arduous permitting for small businesses; a deal to increase the amount of affordable housing in a Divisadero Street development (though her opponents say it still wasn’t enough); and a program to create a “safe” parking lot near the Balboa BART Station to house homeless people who live out of their vehicles — as she and her mother did for years.

But one of her biggest promises has yet to materialize: open a Navigation Center or homeless shelter for youth in District Five. Finding a site for a homeless shelter is one of those tasks, she said, that is way easier said than done.

Her inability to open one has frustrated many in her district.

“I’ve been disappointed in our supervisor. ... Her major achievements are conservatorship and the RV Navigation Center — but that’s 35 people served annually,” said Christin Evans, a bookstore and bar owner in the Haight, and neighborhood activist. “That is just too little, too incremental.”

Despite her critics, Brown’s support of market-rate and affordable housing has won her the endorsements of big names like Sen. Scott Wiener and Assemblyman David Chiu, both Democrats from San Francisco. She also has endorsements from the San Francisco Democratic Party, YIMBY Action, and the S.F. Building and Construction Trades Council.

Her campaign raised $178,026 by the latest campaign finance deadline and received $152,500 in public financing, according to the Ethics Commission. Independent expenditure committees called International Brotherhood of Electrical Workers PAC Educational Fund and San Francisco Fire Fighters Local 798 PAC have also spent thousands of dollars on her behalf.

While a number of board members have endorsed Preston, Brown’s colleagues describe her as thoughtful — someone who cares more about the neighborhood than about political drama. But in Preston, some of her colleagues see a supervisor who would take a more aggressive approach.

“The biggest reason why I endorsed him ... is that we really share a passion for big and bold structural change to the major problems that we’re facing in the city,” said Supervisor Hillary Ronen.

Some also want a colleague more independent from the mayor, so the progressive majority can continue to drive its agenda. Breed doesn’t have many allies on the board, but Brown is often considered one of them.

There have been times that Brown has been aligned with Breed, but she’s also strayed, she said. To the mayor, the supervisor is “Switzerland.”

Dean Preston: He says San Francisco doesn’t have time for incrementalism. He wants big, bold change and doesn’t care that his critics say his proposals — like free bus service for all and 10,000 units of affordable housing within 10 years— sound unrealistic.

Actually, he said, he even welcomes that criticism.

“We are shooting for big things, but those things are totally obtainable — they just require a shifting of priorities,” he said.

He’s a tenants’ rights activist, well known for writing Proposition F, the June ballot measure that gives tenants facing eviction the right to a lawyer. The founder of Tenants Together, a statewide renters’ rights group, is also a homeowner on Alamo Square.

While Brown presents herself as a locally focused activist, Preston is allied with a national movement — Democratic Socialism — that’s pushing Medicare for All, tuition-free college and the Green New Deal.

By associating himself with that label, Preston said he is telling voters that he will prioritize the community over corporate interests and disrupt the status quo. His supporters say he would be a hard-charging supervisor who would balance the needs of the neighborhood, with the larger issues facing the city.

“When times are bad, it is a very powerful message to say ‘There is a problem and the problem is City Hall — and I’m not in City Hall, and I’m going to change it,’” said McDaniel, the political science professor.

But his critics most counter his stance on housing. His proposal to build 10,000 units of 100% affordable housing within 10 years would be unrealistically expensive, they say. It’s proposals like these, his critics say, where Preston’s campaign is too pie-in-the-sky.

“Preston talks about 10,000 units of social housing, but that costs billions and billions of dollars that we don’t have. I don’t consider that a realistic solution,” said Corey Smith, deputy director of the San Francisco Housing Action Coalition.

To that, Preston says, “Why not try?”

Preston’s addition to the board would tip the already-progressive board more toward the left. That could mean more proposals for San Francisco that seek wholesale change in the city — like his idea to propose a ballot measure that would raise taxes for free Muni for all.

It could also spell trouble for Breed.

Preston lost the seat in 2016 to Breed by only 1,800 votes out of 41,000.

If he’s on the board, he said, he won’t be afraid to buck the mayor, but he would also try to build a relationship with her. As of the latest campaign finance deadline, he raised $143,360 this year and received $155,000 in public financing. Preston is endorsed by progressive organizations such as the Democratic Socialists of America SF, San Francisco Tenants Union and National Union of Healthcare Workers.

Supervisor Rafael Mandelman said while he loves working with Brown, he endorsed Preston because he respects his moxie and they have longstanding ties. If he’s elected, however, Mandelman said he is unsure whether Preston would be able to work with the mayor as well as Brown has.

“Mayor Breed’s life definitely gets a little harder if Dean Preston joins the board,” he said.

Trisha Thadani is a San Francisco Chronicle staff writer. Email: tthadani@sfchronicle.com Twitter: @TrishaThadani