I've killed them with both, but I don't want to downplay the challenge of hunting turkeys and say that one way is easier than the other. With that said, the gun gives you a little more room for setup errors. Meaning that, when I hunt them with my bow, it's out of a ground blind. Setting up the blind in the perfect spot is sometimes challenging, and repositioning during the hunt is just about impossible. With the gun, you can setup quick, move quickly if needed, and your range will be greater with the gun. Good luck.
"He who knows nothing is closer to the truth than he whose mind is filled with falsehoods and errors." Thomas Jefferson