The debate on women and work is only beginning. Women can’t have it all? Or is it the case that they won’t take it all?

Anne-Marie Slaughter

First came Cherie Blair’s hot-button comments about working women and motherhood, at the Fortune Most Powerful Women conference in London last week.

Then came an Atlantic magazine cover story, “Why Women Still Can’t Have It All,” in which Anne-Marie Slaughter, once a senior adviser to Secretary of State Hillary Clinton, challenges employers to enable well-educated, stressed-out working mothers like her to reach the top and stay there.

Now a debate is raging across the Internet: Who is to blame for the gender gap at the top? As Slaughter places the blame squarely on companies and policymakers, the unintended consequence of her incendiary article is that she is suddenly being viewed as the anti-Sheryl Sandberg.

Sandberg is the COO of Facebook (FB) who has, in the past two years, become the leading advocate for women taking responsibility for their own work-life balance problems. In “Don’t Leave Before You Leave,” an article she wrote for Fortune in 2009, Sandberg called for women to step up bravely to job opportunities. As she has spread her message at colleges and conferences, the 42-year-old mother of two has practically built a second career as an evangelist for aspiring women.

Even as one of Sandberg’s speeches has attracted more that 257,000 views on YouTube, Slaughter has a problem with the Facebook executive’s call for women to resist “leaning back” in their careers: “Although couched in terms of encouragement, Sandberg’s exhortation contains more than a note of reproach,” Slaughter wrote.

Is this a “face-off,”, as the New York Times proclaimed, between two elite, superstar women about what is right or wrong with workaday lives and careers? “It’s a debate about how we solve a common problem,” Slaughter said Sunday afternoon, talking on her cell phone in her car after dropping off the younger of her two teenage sons at summer camp. Sandberg’s focus, women’s lagging ambition vs. men (“We will never close the achievement gap until we close the ambition gap,” she has said), “is a much, much smaller problem than our social and political structures,” Slaughter contends. Sandberg’s message, she adds, “isn’t taking account of the full spectrum of women who are not superhuman and rich. Sheryl Sandberg is both superhuman and rich.”

Yes, this is a face-off. Sandberg declined to comment for this story–or talk to Slaughter, who says she did not try to contact Facebook’s No. 2 executive until after her article was published last Wednesday. The two powerful women have never met.

But Slaughter would be wise to reconsider Sandberg’s viewpoint since evidence substantiates her theory of an ambition gap. In a recent McKinsey survey of managers at 60 companies including Coca-Cola (KO), Ford Motor (F) and Fortune‘s parent, Time Warner (TWX), 18% of women said they aspired to the CEO position. Meanwhile, 36% of men coveted the top job. McKinsey found that many high-potential women settle mid-career for staff roles–which generally don’t lead to the corner office–while guys gun for stretch positions.

And at last week’s MPW event in London, more indications of the female ambition deficit: In a discussion about leadership moderated by Fortune Washington Editor Nina Easton, Blair, who is a lawyer and a mother and the wife of former PM Tony Blair, pointed out that most women are “too nice” to fight for big salary increases. Susan Gilchrist, CEO of PR giant Brunswick, added, “Women have to prove themselves to themselves to have the same level of confidence that men have the moment they drop out of the womb.”

Sonali de Rycker, a London-based partner at the Silicon Valley venture capital firm Accel, noted that many of the qualities that make an entrepreneur successful tend to be male. While men promote their dreams, she said, women tend to sell the reality of what they’ve already accomplished.

No wonder the Fortune 500 has only 18 female CEOs, while just 14% of Fortune 500 executive committee members are women.

Facebook COO Sheryl Sandberg

If companies enabled ambitious women via flexible hours and other family-friendly programs, these numbers would improve dramatically, Slaughter believes. Her article, which broke traffic records on the Atlantic website, also brought hundreds of emails into her mailbox at Princeton, where she teaches politics and international affairs. (She lists her email address on the University website.). One 33-year-old woman lawyer told Slaughter that she wanted two things: a second child and the general counsel job at her employer. When the woman asked to work from home one day a week, her bosses said no and selected an outside candidate for the top legal job. “That is totally absurd,” says Slaughter, adding “Men are on planes one day a week.”

Slaughter says she has heard countless similar stories from aspiring women denied the conditions they need to move up and remain there. No question, glass ceilings persist at many companies. And it is the rare workplace where the band of acceptable behavior is as wide for women as it is for men. (Hard-charging women tend to be viewed as unlikable by both male and female colleagues.) As for Sandberg, she, in her public talks, acknowledges the institutional barriers. But the systemic blocks are not what she spends most of her time talking about.

Slaughter and Sandberg should meet. I’ve known both of them for several years, and they are not only smart and relentless when committed to a cause. They are, as Slaughter says, “two very successful women who want the same things. We just have some disagreements about where the problems lie.” In sync—or if not in sync, at least in collaboration—these two leaders could help aspiring women and the powers that be build an environment of equal opportunity