On Tuesday, a week after Elon Musk's big Mars reveal in Guadalajara, Mexico, Boeing Chief Executive and Chairman Dennis Muilenburg was asked what big innovations his company had planned for its second century of operations. After ticking off a list of flight and aerospace innovations, Muilenburg came to deep space exploration. "First person on Mars. I'm convinced that the first person to step foot on Mars will arrive there riding on a Boeing rocket," Muilenburg confidently said during a Boeing-sponsored tech summit in Chicago called "What's Next."

It doesn't manifest itself publicly all that often, but there is an intense rivalry between Boeing, a blue-blood government contractor with a long history of aerospace firsts, and SpaceX, which has come along in the last decade and threatened the larger company's space business by offering discounted spaceflight. About the closest thing to trash talking came in 2014, when John Elbon, the head of Boeing's space division, compared the two companies by saying, "We go for substance. Not pizzazz."

Boeing, of course, won't be sending anyone to Mars without collecting tens of billions of dollars in federal contracts for its Space Launch System rocket, for which it is NASA's prime contractor. An Ars analysis found that NASA will spend about $60 billion developing and flying the SLS rocket before there's even the possibility of landing four to six humans on Mars in the late 2030s, and that does not include the expense of spacecraft, deep-space habitats, and accommodations on the surface of Mars.

During his remarks last week, Elon Musk laid out an, at times, ambitious and fantastical plan to colonize Mars over the next 100 years. His Interplanetary Transport System would not transport a handful of astronauts to Mars, but 100 colonists at a time. The rocket powering it would be four times more powerful than the most robust version of the SLS rocket. And Musk said it would only cost about $10 billion to launch the first colonists to Mars sometime in the 2020s.

Critics have called Musk's plan unrealistic, but his vision highlights an inherent tension between "old space" companies like Boeing and "new space" companies like SpaceX. Before SpaceX came along, Boeing and other traditional space firms were accustomed to large, cost-plus contracts to help NASA carry out its exploration program. Musk is trying to change the paradigm. On Tuesday, Boeing's CEO made clear who he believes will win this 21st century space race.