F. Scott Fitzgerald defined high intelligence as the ability to hold two opposed ideas in one's mind and still function. By that measure, an American population in love with both Pope Francis and Donald Trump approaches genius.

The pope and The Donald have been chasing each other off front pages all month: hordes of zealous supporters flock to their appearances and hang on their pronouncements. Yet the leadership ideals they represent could not be further apart. "The superego and the id," "Goofus and Gallant," and "simple sugars and complex carbohydrates" are just a few of the metaphors leadership experts produced when asked to compare the two. "Maybe it's like people sin on Saturday night and that creates business for the church on Sunday," jokes Stanford management professor Robert Sutton, when asked to explain how one person can embrace both.

More substantively, Trump embodies the aggressive, authoritative leadership of the past while Pope Francis represents a more contemporary empathetic and collaborative style, according to John Gerzema, co-author of The Athena Doctrine: How Women (and the Men Who Think Like Them) Will Rule the Future. "The very nature of power is shifting from control to influence," says Gerzema. To compare Trump and Francis "is the study of a 20th-century guy versus a 21st-century guy."

The experts predictably surfaced dozens of differences between Francis and Trump. But they also brought up a surprising number of similarities suggesting that when it comes to what we want from our leaders, Americans may be less conflicted than it appears. Here's what the lion and the lamb have in common:

1. They are authentic.

Trump plays footsy with the truth, but he's forthright about his character. "He is the very worst example of what an American is, but in the moment I can't help but be drawn to him," says Sutton. "There is something emotionally authentic about him even though he is full of shit." (Sutton is especially proud of a Doonesbury comic that cites his book The No Asshole Rule in the context of a Trump candidacy.) Michael D'Antonio, who spent close to 10 hours in one-on-one interviews with Trump for Never Enough: Donald Trump and the Pursuit of Success, puts it this way: "Donald is all Donald, all the time. And I think Francis is all Francis, all the time." (D'Antonio's previous book was about sex scandals in the Catholic Church.)

The difference is that while Trump and Francis are both "authentic as leaders," only Francis is an "authentic leader," says Ronald Dufresne, an associate professor of management at St. Joseph's University, in Philadelphia. "To be an authentic leader you have to be both true to yourself and true to some moral purpose that is important to others," says Dufresne. "The pope is a servant leader, and his higher purpose is to call people to God. I think Donald Trump cares more about the polls than the purpose."

2. They are dealmakers.

Trump's first book was The Art of the Deal. He built his empire by thinking big, calculating the odds, and steamrolling to triumph. Who better to sit across the table from recalcitrant world leaders, he argues. The candidate's latest proposition is his boldest: Vote for me and you can stop worrying. I will fix everything.

But Francis is just as good a dealmaker -- maybe better. Positioned between a rigid church and an increasingly liberal flock, he has had to be, says Gerzema. "The pope is trying to strike deals to get both sides to be a little bit more reasonable and accepting of change," Gerzema explains. "To the church it's, 'We've got to put this chapter of pedophilia and other abuses in the past and reach out or we are not going to have membership.' To Catholics, the deal is, 'Yes, we are going to start to move. But this is a glacier.'"

3. They are populists.

Francis's embrace of a severely disfigured man in St. Peter's Square two years ago touched the world. Advocacy for the poor and marginalized is his hallmark. By contrast, no one expects Donald Trump to treat the squeegee guy wiping the windshield on his Rolls to breakfast at Denny's. Yet he promotes raising taxes on the rich and portrays himself as anti-elitist. "Other than to say, 'I went to Penn and I am a very smart guy,' he does not want to be associated with the intellectual and the artistic," says D'Antonio. "He's like the titans of the Gilded Age, who left things like that to their spouses. He is a man of action."

But Trump and Francis are very different kinds of populists, says Michael Maccoby, an expert on narcissistic leaders, whose most recent book is Strategic Intelligence: Conceptual Tools for Leading Change. "Trump's populism feeds on resentment, on people who feel they've been left behind by the rich and their puppet political leaders," says Maccoby. "The pope's populism is responding to people's hope for a more kindly world and a religion that's not based on strict morality but on care for people in need."

4. They are mavericks.

The Catholic Church and the Republican Party are both venerable institutions. Or, as Sutton puts it, "old, codified bureaucracies constructed by insiders with power." Rich enough to finance his own campaign, "Trump is just ignoring the message that the people who have money want," says Sutton. That includes taking anti-party positions on issues like taxes and universal health care.

While the Constitution under "Anchor Babies" Trump is under threat, church doctrine under Francis is not. Still, the pope "is not afraid to take on entrenched interests," says Dufresne. Vatican Bank reforms and an environmental encyclical that bashes unbridled capitalism are just two of Francis's shots across tradition's bow. "I love reading about him as a radical leader, because the Latin root of that word means to get back to the roots," says Dufresne. "Francis is radical in that he is getting back to love and care and concern for the poor."

5. They are charismatic.

Trump is loud. Francis speaks softly and carries a big ferula. But both are emotionally compelling. And both understand what their audiences want -- or in the pope's case, need -- to hear.

Maccoby says that charisma is not solely an inner trait but also something produced when a leader connects with followers. The leader "becomes more secure and feels he can be more spontaneous, more expressive," Maccoby says. Trump's charisma did not emerge during his earlier flirtations with the presidency because, back then, he did not connect with anyone. That's one reason his present broad and powerful appeal comes as a surprise. "If Donald Trump loses his constituency," says Maccoby, "his charisma will disappear."

The pope's charisma is more sustainable, says Maccoby, because it emerges from a message that is "profoundly Christian and elicits a really deep response in people."

6. They are fearless.

"Donald is fearless when it comes to saying what is on his mind and getting what he wants," says D'Antonio. "Francis is fearless when it comes to opening his heart."

Of course, it's one thing to compare leadership styles: quite another to choose among actual leaders. Click here to find out who would fare better if Francis were to run against Trump for the presidency.