My first experience with Edgar Rice Burroughs' Mars series was my mother reading them aloud to us. I think it was in our double digit years but before we were teenagers, so probably about 8 years ago at the very least.
I've grown up a lot, and, though I still enjoyed A Princess of Mars as swashbuckling daring, I found it disappointing Science Fiction compared to others that I have read.
I think that Burroughs missed many opportunities to flesh out the different Martian cultures -- for example, Green Martians have another set of limbs between the legs and the arms: how does this affect their fighting style, what sort of weapons would they make to accommodate the limbs, etc...
Red Martians are portrayed as the more civilized of the two, yet even the Red Martians are quite war like. I think it would have been interesting if the races had been more 3d.
Asimov described science fiction as a reaction to superior technology -- I would also like to add that it is a reaction to the culture. However, John Carter doesn't really have to do that for two reasons:
1. In the case of the Green Martians, he is already their superior. Since they are a war like race (multi-limbed Spartans!), they value physical prowess. Since the gravity on Mars is lesser than gravity on earth, Carter can easily make 50 foot leaps. Since he is stronger, his blows also hit relatively stronger. There is no reaction to be had because they are beneath him in every way.
2. The Red Martians are very similar to humans: sure they lay eggs, but they have the same number of limbs as an earthling, have family units, create, study, and are, compared to the Green Martians, civilized. In fact, regarding families, Carter was of the opinion that the lack of a family unit among the Green Martians contributed to their war like ways.
In short, John Carter is not forced to question anything -- he embraces the Red Martian as being most familiar, affirming his own assumptions both on Earth and on Mars (which leaves its own implications regarding tradition, culture, that sort of thing). There is nothing that really causes him to pause and to question himself.
Compare to Heinlein's Stranger in a Strange Land where Martian philosophy was devoutly explored and how that related to Earthlings (water brothers to sex to poly-amorous relationships). Burroughs doesn't really use A Princess of Mars to explore social norms (whether different or earthly traditional), political thought (other than the obvious "savagery is bad" sort of thing), etc.
However, that said, I still enjoyed it as a pulp adventure story, just a bit deficient in the Science Fiction Exploration of the Soul department -- which, apparently shouldn't be such a surprise. According to Wikipedia (I know, I know), it's actually a Planetary Romance. *shrug* Who knew?
Also, I had forgotten how many times Dejah Thoris was put on a pedestal with her beautiful face and her perfect lips, and her slight, girlish figure. Perhaps she and Edward Cullen should meet. ;)