The two men running for lieutenant governor in Virginia both live in Hampton Roads. They were both in the military — Republican E.W. Jackson was a Marine, and Democrat Ralph S. Northam was an Army doctor. They both say they want what’s best for Virginia.

But the men have starkly different backgrounds, styles and political approaches.

The campaign for the No. 2 job in Richmond is usually something of an afterthought. But Jackson has proved to be a provocative figure, not only for the conservative activists who enthusiastically embraced him at the GOP’s nominating convention in May, but also for a host of opponents.

Jackson, a minister at a small Chesapeake church, can be a fiery public speaker. Northam, a child neurologist, tends to be lower-key.

Jackson is known for controversial rhetorical flourishes. He has called the idea that President Obama is Christian “laughable.” He said gay people’s “minds are perverted. They are frankly very sick people psychologically.” And in a sermon in September, he said non-Christians “are engaged in some sort of false religion.”

On the campaign trail, Jackson has often sought to nationalize the race, even acknowledging that his staff sometimes has to remind him to talk about Virginia. But the United States has lost its way, he says, claiming an insidious influence of Obama and other Washington officials on the spiritual and economic life of Virginia.

Northam, meanwhile, has warned that Jackson is emblematic of a rigid and divisive social agenda that has hurt Virginia’s national standing and at times made the commonwealth a national punch line.

The role of the lieutenant governor is to preside over the Virginia Senate, and, in some instances, to cast tie-breaking votes in the evenly divided body. It is also a steppingstone to the governor’s office.

At a Norfolk debate, the candidates challenged each other on their approaches.

“What we don’t need in the Senate is someone making comments about other folks’ religion that are offensive. We don’t need people talking about others’ sexual orientation,” Northam said. “I would suggest that right now there are 20 Democrats in the Virginia Senate. Making statements such as that we’re anti-God, anti-family and anti-life are offensive. They’re divisive. There’s no place for them in the Senate. And there’s no place for them in Virginia.”

Northam added: “We need people who are moderate — like-minded people who can sit down at the table and think about what our challenges are and what solutions we have . . . and get things done. That’s my reputation in Richmond, and that’s what I plan to do.”

Jackson said his statements should not be used to undermine his candidacy.

“The Founding Fathers said a person’s religious opinion should not be held against him in civil discourse and should not be a disadvantage to him in civil discourse,” Jackson said. “I will be the lieutenant governor of all of the people of Virginia — black, white, brown, you name it, rich, poor, no matter their sexual orientation. That’s the role of lieutenant governor. You work with everyone — Democrats, Republicans — and I want to do that, because I think we desperately need to come together.”

Northam became a member of the Virginia Senate in 2008 and represents parts of Norfolk and Virginia Beach and all of Accomack, Mathews and Northampton counties.

In 2011, Jackson ran for the Republican nomination for the U.S. Senate in the 2012 election, receiving 4.7 percent of the vote.

The candidates have far-reaching policy differences.

Jackson has called abortion a “genocide” of millions of black babies and said, “Planned Parenthood has been far more lethal to black lives than the KKK ever was.” A group Jackson founded, Staying True to America’s National Destiny, has called for “an end to all abortions” and maintained that “to kill babies for our convenience is the equivalent of an idolatrous offering to the god of ‘sexual license.’ ”

Northam supports abortion rights. He was a leading opponent of a Republican bill last year that would have required women to undergo an invasive procedure known as a transvaginal ultrasound before some abortions. Activists — and late-night TV comics — seized on the proposed requirement, which was eventually dropped.

On the environment, Jackson argues that Virginia’s Department of Environmental Quality is doing the bidding of the Environmental Protection Agency, to the detriment of industry and local coal miners. Northam emphasizes his legislative efforts to clean up the Chesapeake Bay.

Jackson wants to eliminate the state’s corporate income tax, which he says will boost jobs and growth. Northam argues such a move would bankrupt the commonwealth, and instead calls for improving Virginia’s aging infrastructure and extending pre-kindergarten education statewide, although he doesn’t cite a price tag on that major initiative.

They also diverge sharply on education.

Jackson advocates using public vouchers for private schools and using funds usually set aside for public education to benefit parents who home-school their children. Northam said such moves would shift more than $100 million from public education and lead to 1,700 teacher layoffs if other funding wasn’t brought in to make up the difference.