In zeolites and synthetic resin method which will be more efficient in removing permanent hardness of water:

The difference between the zeolite and ion exchange process is that the zeolite process uses the mineral zeolite as the exchanging resin for cations in the hard water whereas the ion exchange process include several different resins for the ion exchange.

∴ Synthetic resins method is more efficient as it can exchange both cations as well as anions.