They look more like some high schoolers to me I expected them to be really tall and muscular, instead they look like Beverly Hills 90210 cast. I like how constantly the girl and her pals shout "Mars, Mars, Mars!" and then is slapped around by the commander of the ship "no, today you won't fight Earthers, instead you will escort space hillbillies to some ice asteroids". Which I think is the real place where this quarrelling bunch should be. And when I read spoilers of what will happen with them afterwards, I can just say that well, no beep wonder.
On the other hand, it's as good a depiction of young uber-patriotic wannabe badass marines who have never seen action but crave for it, as you can make

hmmm, very apt comparison!
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Compare it with France and England in the 19th cerntury: France was stronger (more people, richer) but was land based, Britian however was a naval power and controlling the seaswe know the end of the story.
Earth is like Franve, Mars like Britain.
And sapce has become what were the seas in the 19th century.
They might unable to invade (all of) Earth, but they can cut off the supply lines from the Belt.
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If I understand it Earth is richer, they have better weapons? Plus Earth soldiers are stronger
Earth is probably richer, yes. Mars had to postpone their terraforming efforts for a number of years in order to focus on building up their military.
While any gun can kill in that sense, Mars equipment is generally superior to Earth equipment (especially in terms of ships). Mars has the technological edge, Earth has the numbers.
A soldier from Earth would also be inherently stronger than a soldier from Mars, yes (due to gravity). To combat this, Martian marines always trains in 1G to be physically equal to their Earth counterparts. A Martian marine is widely considered quite a bit superior to their Earth counterpart.
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It seems like Earth has more resources but Mars has a more professional military
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As I understood it Mars ships are newer and more advanced (Stealth), but Earth is superior in numbers.
It was also siad that Mars soldiers always train under 1G conditions.
But look how the Belters kicked the asses of the Martians albeit they can't even live on Earth.
Better training and equipements nullifies most if not all advantages of Earth soldiers. In space their need for higher gravitation might even be a huge disadavantage. Maybe that's why their ships are inferior to Mars ships for their design and energy efficience is negatively affected by the need to provide 1G most of the time.
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It is hard to compare Mars to US before WW2, as US were already superior to any other nation, they just had not had put their war manufacturing in the highest gear. But if we look at GDP and all other indicators, US became the top world superpower sometime after WWI already. Sure Britain still had an empire but these were mostly poor countries that UK had to support, more of a strain on Britain than anything else.
Maybe Mars can be compared with Nazi Germany vs USSR/Britain. Numbers are on opponents side, but new technology and will to fight and prove themselves (at least at early stages of war) on Nazi side.
Of course Earth still has massively bigger ability to build actual stuff and allocate resources for military needs, so if Mars did not win decisively in early stages of war (like Germany vs France in WW2), they'd be in for a load of pain. Similarly how Nazis just kept winning battles vs Soviets in the early stages and Soviets just put in more and more men and tanks on the battlefield. Both were bleeding out, but Germany much more so

Well we DID win WW2. We liberated Europe by way of Normandy, and then we hit Japan back with a fat man and a little boy.

I get the sense that Mars is supposed to be the "young and cocky" military power. Their military strength hasn't truly been tested yet but they're convinced they can win any war. They're like America in WW2.