Military
Mars has fewer ships than earth but their technology is more advanced compared to Earth's ships. So, it's really like a quality vs. quantity thing. Same with the infantry. Mars is aware that they have fewer infantry men but the ones they have are equipped superb,superbly; e.g. Bobby Draper (she's the top notch).
Economy
Mars has a common goal to make their planet habitable, everybody is working and basically nobody is unemployed. While Earth has way more resources in termterms of manpower, they also have a very high unemployment rate and have to spend considerable resources to simply feed people not working. This problem on Earth is so gigantic, that people that want to study, first have to work for a year in any job to prove that they are willing to work before being allowed tointo a university.
Conclusion
Earth could probably crush Mars in an economic sense, also due to the fact that Mars is still purchasing air from Earth in order to survive. However, it is more of a cold war than a real war and they compete but don't try to annihilate each other. In a military sense, it is unclear who would win. Mars with their fewer but better ships or Earth with a bigger number. However, when Bobby Draper is on Earth, she wonders if Mars could ever win a ground battle on Earth as there are simply too many humans on Earth and they could crush any invading Mars force butby sheer numbers, even if Mars deploys their best tech and Earth only has sticks and stones.