It's been a while since I read A Princess of Mars due to my focus for a while on watching movies I had never seen, but should have. When my Archos died I went back to the Kindle for now, and picked back up with the next book in the Barsoom series, Gods of Mars.
In a lot of ways this book is a better one than the predecessor. It's as if the author is more confident and doesn't need to pull his punches. He also doesn't need to contrive a reason to end the story at the end of the book, since now he's confident he can go on to a third one (a similar phenomenon is often seen in the second movies of a series).
Where sequels like this often fall down is neatly avoided here. Often, the first book is full of a sense of the wonder of discovery, as we learn of a new land, and meet the people, and discover how things work. The first book certainly derived a lot of its magic from that. But often the first book also establishes too much of all this, in the process of ensuring we know everything we need for the story to happen, so there's not much left to discover in the second book.
At the end of the first, I might have guessed this would happen, but Burroughs is able to spend most of the book in parts of Barsoom that were barely hinted at in the first book, yet which do not contradict it, or seem tacked on, since they were hinted at. I don't think he can do this too many more times, though. Another book or two and he'll either be retreading, or stretching things too thin, or making it seem too contrived that there's yet another layer of secrets behind the others on Barsoom. I wouldn't be surprised if the books start to feel flat after another few, or sooner.
As before, he uses remarkable coincidence shamelessly. Our hero never walks blindly into a room without finding precisely what he was looking for, or the one person out of five million with whom he has a relationship, or the sole member of a species who thinks differently from all the others. What's particularly galling about this is that sometimes John Carter explicitly alludes to it -- he casts himself to fate, counting on it to provide something -- but other times he's as dense about it as a committee of rocks. Through about a third of the book, a revelation about another character so obvious I twigged to it literally on the second sentence of the character's appearance kept failing to make an impression on thickie Carter (and fate kept goofing on us by having the character about to say something that would make Carter have to figure it out, only to be interrupted at the last moment).
If I had to criticize the book, I would say that some of the grander scope that Burroughs undertakes gets a little tiresome. In his defense, when he describes a vast war of thousands of airships, he doesn't drag it out nearly as long as many modern authors, let alone older authors. (Jim Butcher would have filled three chapters with one airship battle that Burroughs knocks out in about two pages, particularly if it occurred in his Alera books, where he seems far more prone to that kind of self-indulgent blather than in the Dresden books -- or maybe it just seems that way because of how much more compelling the setting and characters are in the latter than the former.) Even so, sometimes it seemed like we spent too long on the actual war of all these warlike people. The first book had plenty of that, but it was always more personal; we saw it from the perspective of a few people in the middle of it, not a general floating above it, so we focused on the action of being in the thick of it, not the drier tactical stuff. That happens a lot in this book too, but once in a while, it meanders off into more tedious topics.
Overall, though, Burroughs seems to be more confident, and more ready to take what's good in the first book and add more spice to it. More political intrigue (but not enough to bog things down), more world-spanning action, and more message (though he dabbles a bit in heavy-handed pontification against religion and superstition -- a welcome message, but it gets repeated just a little too much).