Hevi is going to do a lot of things better than lead. However both will do the same and that's kill turkeys. It's a matter of preference. I use to shot hevi but went to longbeards and like them. Price was a deciding factor there.
However just set up a 20 gauge and gonna shoot blends and the heavyweights in it.
Now that I've muddied the water shoot what makes you happy but don't listen to any advise that degrades lead or claims it just don't kill turkeys anymore. As a hunter just pattern your gun, keep your shots at a ethical range, and enjoy turkey breasts for lunch. Regardless of shell type!