How many spokes in the old and new wheels? The number of spokes will make a difference, and the rider's style will make a difference. Definitely harder on spokes to hammer up hills in a high gear. Also easier on spokes if the rider gets off the saddle for bumps and potholes.

Double walled vs single walled rim shouldn't make a difference unless he was breaking spokes next to the rim, but that would be unusual. The old wheel could have been poorly made, with hub flange holes too big for the spokes. Or the rim could have been a little bent, causing unequal spoke tension.

Good luck with the new wheel.