In comparison to the zeolite process for the removal of permanent...

Zeolite removes only cations from hard water, as given below by reaction:

$2NaZ + {M}^{+ 2} ( aq ) \to {MZ}_{2} + 2{Na}^{+}HereM - Ca, Mg$

While, synthetic resin removes both cations and anions, as given by following reactions:

For cations-

$2RNa ( s ) + {M}^{+ 2} ( aq ) \to {R}_{2}M ( s ) + 2{Na}^{+} ( aq )$

For anions-

${RNH}_{3}^{+}{OH}^{-} ( s ) + {X}^{-} ( aq ) \to {RNH}_{3}^{+}{X}^{-} ( s ) + {OH}^{-} ( aq )$

So, synthetic resin method is more efficient as it can exchange both cations as well anions.