Heavi-shot/ tung based shot is popular for turkeys (ducks too) because it adds range and penetration to your shotshell/gun.
The space metals are harder and denser than lead. Because they are harder, they do not deform easily (if at all) upon firing, and allegedly fly truer, thus denser patterns.
Since they are heavier than lead, when started out at the same velocity, they retain velocity better at range, increasing penetration.
Guys that are shooting them tell me they add 10-15 yds range onto their shotguns performance. Maybe more.
I have not made the switch, since I'm doing just fine under 45 yds w/ lead.