Turkeys are not hard to kill if you hit them in the head/neck. One BB will do the trick many times. Shoot an adult Tom in the body and odds are the turkey will fly/run away and become coyote bait. IMHO, There are three reasons folks miss or maim turkeys and the type of gun/shell they are using ain't one of them.
1.) The hunter does not pattern his gun with the shells he is using. This means he does not only not know exactly where the gun shoots with that ammo, he also is not aware if there are holes in his pattern. Pattering a shotgun is a learning experience to those who have never done it. Patterns with different loads can be like day and night and many times do not shoot to POA. One reason why sights on turkey guns as opposed to just the bead are so popular.
2.) Folks do not shoot at, or do not have a clear shot at the head/neck area. Shooting a turkey in the body, even at close range with birdshot is fruitless. Their wings are like body armor and many times even when mortally wounded will fly or run a good distance. Unless they go down in a green field, their natural camouflage makes them tough to find without a dog. Folks many times make the mistake of shooting right at the head which gives them a very small margin for error or a good chance the head will be in a hole in the pattern. Shooting at the neck gives more margin for error, especially if the bird is above or below you. Other mistake many make is shooting at the bird when in full strut. When in full strut and the head and neck are pulled tight against the body, the target area is not only very small, but protected by those body armor wings. Straight on is a little better, but waiting till they at least come partially outta strut and raising their head/neck is better. Waiting till they come fully outta strut and extending their head neck in search for the calling hen is preferred. A single cluck works well for this.
3.) Misjudging distance. Watching a strutting Tom out in an open field, dancing for his hens, is an awesome sight. Calling one in and having them do this makes one's heart pound and excitement level jump. But a strutting Tom is purposely making himself look LARGER. Larger objects appear closer to us than smaller ones at the same distance. This means a strutting Tom looks closer than the hens with him and looks closer than he actually is. With a rifle on a deer, misjudging distance by 20 yards is a moot point. Misjudge a Tom by 20 yards at the outer limits of your range, means a miss or wounded bird. This is where those super duper turkey artillery shells with the death match widow maker choke tube SOMETIMES help by giving one an extra 5-10 yards of range. Using them as a crutch or an excuse to take shots at birds outta legitimate range again, means wounded birds. Scopes on turkey guns also give the impression they are closer than they are. Watching one come all the way across the field without taking you eye outta the scope means you really do not know how close he is unless you have marked the range. I've been turkey hunting for over 30 years and probably have more than twice that amount of beards in a coffee can. I still take the time on every set-up, even those that catch me off guard and I need to sit right now, to judge and make mental marks of where the bird needs to pass before I have a legitimate shot. On set-ups where I have time and set up decoys, the decoys are a good mark. Sometimes a stick stuck in the ground works. Many times it's just a mental note of a particular cornstalk of patch of dandelions, or a bush next to the lane. I know tho, before the bird comes in, what it has to go past before I take the shot. Every time. Better to let the bird walk for another day, than to wound and lose him or screw the spot up for tomorrow's hunt. Knowing the effective range of your particular gun and ammo and knowing where this is when the bird is in front of you, is paramount.