Have hunted pheasants for almost 30 years. Have never run out of shells on a hunt. So that would not worry me. Reason for the 16 would be sentimental more than anything. But the 16 is a pheasant killer, seen it first hand growing up.
So was my .410, but my success rate went up when I switched to a Winchester 12 side by side, and then to 12 autos.