From a dusty expanse in West Texas, Jeff Bezos and the crew of Blue Origin, his well-funded aerospace company, fire up their New Shepard rocket. It rises vertically, thrusting into the heavens at more than 2,800 mph. The unmanned crew capsule it's carrying detaches and it crests roughly 64 miles above sea level, and the booster begins plummeting back to earth, a pencil dive from space. At 3,635 feet, the engine reignites, blazing a streak at its tail that flares as the rocket nears the ground, slowing its fall. Within a plume of dust, New Shepard softly touches down at around just 4 mph—a controlled test landing that Bezos calls "flawless."

When Blue Origin first achieved this feat in November 2015, Bezos, wearing aviators and a cowboy hat, sprayed champagne in celebration of a landing many proclaimed "historic." By April, when Blue Origin reused the same rocket for the third time, the remarkable had become routine. And soon, old news: On April 8, Elon Musk's SpaceX launched its Falcon 9, a rocket that's substantially faster, more powerful, and larger than Blue Origin's—roughly as tall as a 24-story building. Musk's team not only managed to land the Falcon 9 safely from a higher altitude, it did so on a drone ship floating in the Atlantic Ocean.

Most Blue Origin and SpaceX insiders recoil at the idea of a rivalry, preferring to view their contributions to spaceflight as progress for all mankind. But the fact is that the two companies are engaged in fierce competition: to recruit the best engineers, and, above all, to make history. And their respective leaders, Bezos and Musk, are in the running to be the world's dreamer-in-chief. Let Alphabet CEO Larry Page have his moonshots; this is about Mars. Bezos and Musk are not only competing against each other but an emerging generation of aerospace entrepreneurs, as well as fellow swashbuckling billionaires Paul Allen, Yuri Milner, and Richard Branson, all of whom have private space initiatives. But Blue Origin and SpaceX's more frequent launches, chronicled for social media consumption, have given them the lead in the public's imagination.

Touchdown! Blue Origin and SpaceX each won the Internet on the day when they stuck their landings.Photo: SpaceX, Alamy

Bezos is working toward a space-faring universe where people will live and work. Musk envisions colonizing Mars. To get there, they must first dramatically lower the cost of spaceflight, which is why they're both focused on constructing reusable rockets, vehicles that will make ferrying humans to space more financially feasible.

The two are on different trajectories, Bezos's more gradual than Musk's, say sources familiar with the companies' plans. "Everything we did [at Blue] was thought about in terms of decades. It's very much how Jeff thinks about his companies," says one longtime Bezos confidant. "SpaceX, on the other hand, ran like hell and burned their people out. Culturally, the two places really reflect their leaders." When I ask SpaceX senior communications manager Phil Larson about these charges, he says, "Hours and expectations are higher than the industry average, but you can't make humanity a multiplanetary species on 40 hours a week." (Blue Origin declined to cooperate with this story.)

Musk founded Space Exploration Technologies 14 years ago, and he sunk $100 million, the majority of his fortune at the time, into the risky venture (he invested the rest in Tesla Motors and SolarCity). Even with his team working 90-hour weeks, SpaceX was perpetually on the edge of bankruptcy. "We always had money problems," says one former top engineer who worked closely with Musk. "We had this tremendous burn rate, but to get anything done, Elon had to hire lots of people." Although three launches ended in failure, the company's fourth was successful, and SpaceX ultimately won a $1.6 billion contract from NASA in late 2008, effectively saving the company. By 2012, SpaceX began flight testing its reusable-vehicle system.

Bezos founded Blue nearly two years before SpaceX began, but pursued a more methodical approach. (He wears cowboy boots emblazoned with Blue's motto, GRADATIM FEROCITER, which means "step by step, ferociously.") For years, the company employed just a few dozen staffers, keeping expenses in check (today, Blue Origin has a team of approximately 600 to SpaceX's more than 5,000). They worked tirelessly—Blue ran into a series of setbacks before its New Shepard system made strides in more recent years—but their situation was simply less urgent than SpaceX's. "Elon had to get to revenue or they wouldn't survive, whereas Blue could go on many, many years without ever having revenue," says a former manager at Blue describing the "luxury" of having a founder as deep-pocketed and patient as Bezos. "But that's why [SpaceX] achieved a lot more in roughly the same time period."

Both Musk and Bezos are known as demanding bosses who have become fluent in their adopted industry's technical intricacies. Musk, who moved certain Tesla operations closer to SpaceX's sleek headquarters in Hawthorne, California, so he could better oversee both companies, is particularly intense, and stories abound of him driving employees to do the impossible. Caught unprepared in a meeting? Musk might cock his head back, his eyes rolling to the ceiling as he decided "how much he is going to unload on you," recalls the former top engineer. "He'd go, 'Did you consider this?' And, boy, if you didn't know what he was talking about, you were in trouble."