Ms. Warren has taken steps that reflect a traditional and practical course. She joined the Senate Armed Services Committee to attain national security credentials. She is privately hosting monthly dinner seminars with policy experts to expand her command of the issues (last week was on Afghanistan and Pakistan and featured Barnett R. Rubin, a New York University-based scholar on the region).

And, as she demonstrated here with a reminder to King’s old congregation that “there’s Jesus in every one of us,” she is opening up about herself to satisfy the electorate’s hunger for personal connection. Maybe even more striking than invoking Scripture, the scourge of Wall Street is spending some time with bankers: She attended a party fund-raiser in July at the summer residence of a former UBS executive, and also this summer she met privately in Washington with JPMorgan Chase’s chief executive, Jamie Dimon.

Mr. Sanders, however, appears to believe that no such nods toward pragmatism or convention are necessary in today’s Democratic Party. He is still surrounded by the same coterie of advisers, is remaining a political independent and is as convinced as ever that people will respond to his well-honed pleas to confront the billionaire class, provide health care for all and offer tuition-free access to college.

To the frustration of some of his advisers, Mr. Sanders has shown no willingness to veer from his social justice catechism to tell voters the personal details of his life’s journey, banking that an electorate that could elect Donald J. Trump to the White House no longer needs such political rituals.

Which of them is better able to broaden their appeal beyond the liberal white activists who crowd their public appearances could ultimately determine their prospects.