Honestly, I like fancy guns, but a turkey gun is low on my to-buy list. I think there's a pretty high ratio of marketing hype to realized benefit, even for guns. Sure, weight can be a factor sitting still for long periods of time, and a short barrel might catch a few less twigs stomping through the woods. But if you're inattentive, careless or noisy you're still going to make a mess of things. I'd just always prefer versatility.
More, some of these turkey shotguns are just looking silly these days. Good for the people that like them, but I just think the AR parts some of these manufacturers are Frankensteining onto their turkey guns are downright hideous. I can't think of a time I've ever said "Darn, I wish I'd put a telescoping stock/pistol grip/target aperture on this 12 gage." And if you need an Eotech using shot at 30 or so yards, the bead sight wasn't the problem. I don't mean to sound so critical - there are a lot of cool, fast cars that are butt ugly also. But I've been fine all along with a decidedly "un-turktical" Mossberg: long chamber, 28" barrel, dirt cheap.