The interesting point: both dual theories are required to reach an interpretation. Witten goes back and forth between them to fix certain parameters, and constrain the form of the CFT.
In AdS/CFT the GKPW formula tells us how to relate observables of coupling fields in the bulk to fields at the boundary.
We understand the concepts of the theories (in part) through understanding their relation to their dual. Also a heuristic tool for theory construction.