The Tales of Ancient Mars look very modern, which means that the Martian civilization is definitely in a decline as portrayed in John Carter's Mars.
There are many elements that are reminiscent to the novel Dune; ecological crisis and the limits imposed to the continued human habitation of the planet. This includes the presence of an environmental scientists that is attempting to establish an atmospheric plant to save mars from it's environmental poisons.
The tales are a great addition to the Martian adventures as envisioned by Burroughs.