I'm beginning to learn AdS/CFT and I have an elementary question. It is said that since it is very hard to calculate 4 point and above correlators in a strongly coupled CFT, we can use instead the AdS/CFT duality to calculate the correlator of the dual field in AdS and take the appropriate boundary limit (that's one way of doing it.)
But we can also use the large $N$ expansion for a strongly coupled field theory. So instead of using the AdS I could directly calculate the correlators in a large $N$ expansion.
So is it that we have 2 different methods for calculating correlators in a strongly coupled field theory? Or are they actually the same method? If they are different, is there a reason to prefer one over the other?