yes, a sync motor has not slip during normal steady state operation.
the sync motor will have some extra cost and complexity associated with the field circuits. it usually isn't justified except the low speed high hp applications where the sync motor may be cheaper (initial purchase) and more efficient. an old thumbrule was these were worth considering when the horsepower was more than the rpm.
the reason is that induction motors pay some penalty in efficiency and power factor for their exciting current necessary to induce a field accross the airgap. This is not much of a penalty for high speed motors where exciting current is low, but it's a big penalty for low-speed motors where exciting current is high.
I would be inclined to suspect a sync motor would be less reliable due to extra complexity associated with field circuits.
