Skyscrapers and giant yachts are so passé. These days a tech billionaire who wants to assert his wealth, power and, er, manhood needs a rocket to play with – and the bigger the better. Two billionaires in particular have been tussling lately over who has the more impressive equipment: Jeff Bezos (above), the boss of Amazon, and Elon Musk (below), the boss of SpaceX and Tesla. As childish as their public sparring appears, the consequences are tangible – and deserve to be widely celebrated.

Bezos made his fortune through Amazon, the retailer whose spookily accurate algorithms know what you will buy next even before you do, and whose cloud-computing systems quietly power much of the internet. With his vast but hidden power and characteristic laugh, it’s surely only a matter of time before Bezos is used as the model for a Bond villain. In his spare time he has been playing with his rocket on his ranch in Texas – a ranch so big that it includes a spaceport. He is also building a giant, indestructible clock inside a nearby mountain that will chime once a millennium (it’s supposed to encourage long-term thinking).

Musk, meanwhile, became wealthy by co-founding PayPal, and ploughing the proceeds into Tesla, which makes ridiculously fast electric cars (they actually have a “Ludicrous” setting that enables them to do 0-60mph in 2.8 seconds), and SpaceX, a rocket company. Musk appears to be the successor to Steve Jobs – the innovator even non-techies have heard of. But Jobs did not crash supercars and fly fighter jets in his spare time, or casually propose a design for a supersonic tube-railway on stilts (which several companies are now trying to build). For the past year, however, Musk has been preoccupied with landing a rocket on a giant, autonomous sea-going barge. After four failed attempts, each of which ended in “rapid unscheduled disassembly”, which is rocket-speak for a “large explosion”, he finally pulled it off in April. In a tweet last year Musk promised that, once he got it to work, “I’m treating myself to a volcanic lair.”

Which brings us to the specific nature of the two men’s rivalry. When it comes to rockets, the hard part is not getting it up – quite the opposite, in fact. Bezos and Musk are pushing the frontiers in reusable rockets, in which the booster section at the bottom returns to Earth after lift off, rather than being discarded in the sea. Rockets are expensive, so throwing them away like that is, if you think about, bonkers: Musk compares it to building a new 747 every time you want to cross the Atlantic. In December last year his company successfully landed the first stage of one of its Falcon 9 rockets on a landing pad in Florida, after it had launched a handful of satellites into orbit. But this triumph was undercut by the fact that just a few days earlier Bezos’s rocket company, Blue Origin, had flown its own unmanned rocket to the edge of space and then landed it back on the launch pad.

Bezos joined Twitter, which he had previously shunned but where Musk has a huge following, in order to announce his triumph with his first tweet. Much passive-aggressive tweeting followed, as the two men outwardly congratulated each other on their accomplishments, while quietly insisting on the superiority of their own rockets. Yes, Bezos may have landed his rocket first, but Musk’s is much bigger and can carry payloads into orbit. Then again, Bezos re-flew his rocket, proving that it was genuinely reusable. That put the ball back in Musk’s court. Which is why he’s so pleased to have pulled off a sea landing of a rocket on one of those giant barges. Next he plans to demonstrate his new, even bigger rocket. Top that, Jeff.

Why should anyone care about this posturing? Because in their one-upmanship, the duelling billionaires are bringing down the cost of access to space. A Falcon 9 rocket costs about $60m, and the booster section at the bottom, called the first stage, accounts for about 70% of that sum. Recovering the first stage and reusing it, say, nine times could therefore cut the cost of a launch by two-thirds. Landing rockets on sea-going platforms helps too: you can devote more fuel to launching heavier payloads if you don’t have to fly all the way back to a terrestrial launch pad afterwards.

Bezos is eyeing the space-tourism market. Musk’s rockets already carry cargo to the International Space Station and launch commercial satellites, but he is looking beyond that to his real goal: the colonisation of Mars, a crazy-sounding plan that he has been going on about for more than a decade. “I want to die on Mars,” he likes to say, “just not on impact.” He believes a Mars colony is a vital insurance policy for mankind, which might otherwise be wiped out by an asteroid, nuclear war or malevolent killer robots. His new Falcon Heavy rocket is due to make its first flight this autumn, and he says he will unveil the plans for a ship called the Mars Colony Transporter in September.

Even if he doesn’t get to the red planet (though my bet is that he will), Musk is advancing rocket technology at unprecedented speed, repeatedly doing things that were previously thought to be impossible. If his rivalry with Bezos accelerates the process, so much the better. If rich men want to compete to make space travel cheaper, that’s great. It’s a productive and useful form of egotism, unlike building skyscrapers or acquiring yachts. And you don’t need to be a rocket scientist to appreciate that.