The pilot of the Piper reported that, after landing, while taxiing back to his parking spot, he saw a Cessna holding short at the intersection to the same taxiway. He did not see the Cessna move so he continued to taxi but then felt a "strong impact" as his airplane passed the Cessna. The flight instructor of the Cessna reported that he was taking a passenger on a familiarization flight. After clearing the taxiway from the ramp, he maneuvered the Cessna to the taxiway intersection. He then saw a Piper airplane taxi past him and believed he had adequate clearance, so he continued to maneuver and turned left on to the taxiway. While simultaneously instructing the passenger during the movement, the Cessna's left-wing tip impacted the Piper's engine and left aileron. The instructor added that he should have waited for the Piper to pass the airplane and should have spent more time briefing the passenger to reduce task saturation. The Piper sustained substantial damage to the left aileron. The Cessna sustained minor damage to the lower engine cowling and propeller. The flight instructor and the pilot reported that there were no mechanical failures or malfunctions with their airplane or engine that would have precluded normal operation.