I didn't see Avatar or John Carter, but from the trailers, I have the impression that Avatar was a major influence on Carter. Yet, one was one the most popular movies of all time and the other one of the biggest bombs of all time. Humans are so fickle.
Anything "alien" is going to be stylistically affected by Avatar. It's the technology. That said, other seminal special effect /cinematography movies include The Matrix, The Mummy, Die Hard, Lethal Weapon, LOTR, Tron, Star Wars Trillogy, Superman, Close Encounters, Alien, Aliens, Blade Runner, Mad Max, Terminators 1 & 2... just to name a few.
Notice though that Stephen Spielberg, Rodger Zemekis, Joel Silver, John McTiernan and James Cameron are involved in many of those films to some degree or another? They are trend setters that are often stylistically copied knowingly or subconsciously from then on out.
Look at war movies post Saving Private Ryan,
then before that Platoon,
then before that Red Dawn,
Before that Rambo,
before that The Deerhunter,
before that The Green Berets,
before that Here to Eternity...
This happens. No surprise. But again, good to know.