I've got both. I like both. Broodies are well, chickens. Don't think just because it's natural that it's flawless, some break eggs, botch hatches, eat or kill chicks, take them out too soon and lose them to 'nature'.
While nothing beats a great broody, I happen to like the total pet nature of what I hatch indoors. If momma raises them frequently they aren't as attached to people. They're much harder to make pets out of. And I LIKE my chickens really tame and my turkeys, for that matter.
I have two broodies going now, and two incubators going now. If anything happened to the broodies - if they quit, give up, kick out eggs, get eaten or killed or die, I can incubate them myself.
Both ways have value. Once these are better at it in fall I'll give them "good" eggs like my turkeys to incubate. But this batch of broodies is new at it, they'll make mistakes in all likelihood.
I like having both available.