Because of its weight, it is very easy to damage lead shot. Damaged lead shoot can hang up in the bore when loaded.
One 2.5" round lead ball weigh 2.5 lbs, 10 balls weigh 25 lbs. One zinc 2.5" ball weighs 1.4 lbs and 10 balls weigh 14 lbs. Moving 25 lbs of lead balls around is a back breaker and increases the likely hood the balls will get damaged. 14 lbs of Zinc isn't any picnic, but moving the balls around isn't going hurt the balls.
It only takes a little more heat to cast zinc.
Zinc shot can often be recovered and reshot. Lead can often be recovered, but it will have to be recast again before it can be reshot.
Using the same loads pressure of course will be higher in the lead loads. You will have to reduce loads substantially for lead. This will result in slower velocities and greater elevation changes to hit targets.
Zinc will preform more like the original cast iron shot being closer in weight.