I'm kind of with you Domestic, not sure whether I prefer the broody or not.
I had my first hatch from a broody last year. It went great, but I didn't like that I couldn't handle the chicks often. But, she's doing her job. She is my "pet chicken" a bantam cochin, so i was surprised last year when she wouldn't let me near her chicks. She taught them that I was a predator. I didn't get any store bought chicks last year.
This year, when she went broody, which didn't hatch, I slipped 4 shipped day olds under her. That was 4 weeks ago, I lost 2 of them, to pasty butt, at least that's what I think it was. She wouldn't let me get a them often enough to check them out. The other 2 are doing fine, she's a really good mama, and chicks raised by a broody are much smarter. Mine doesn't eat that much, I have the problem of her scratching all of the feed out of the feed dish in order to teach her chicks out to scratch for food. I can throw treats in there, and she will peck whatever it is until it's small enough for them to eat, clucking at them the whole time, to come and get it.
The 3 she raised last year, are very smart. 2 hens and 1 roo. He has been my best roo ever. Finding them food, warning them of danger, and has no problem with me.
I have 3 chicks that are a week or 2 older than the 2 she is raising. I thought they were younger when I got them, but they apparently were just enough bigger that she wouldn't have anything to do with them. Kept them with her for 2 nights and 3 days. She kept them warm at night, but kept her "chicks" away from them during the day, and would peck them if they came out to eat. So I decided to separate them.
In this time frame, I also bought 3 twelve week old bantams. So, me, hubby and the 3 bantams have been raising them. I enjoy these 3 chicks so much! i can handle them, they are friendly, though when I throw treats in, they and their 3 banty mama's all look at me like what the heck are we suppose to do with this.
It is really nice with a broody to not have to worry about heat for the chicks. The broody definitely raises them to be smarter. I do separate the broody, since I'm just not set up to keep her in with the main flock. She had a late hatch last year, and ended up staying in my small coop all winter with her 3 chicks.
What I am going to do different this year: Her 2 chicks are going in with the other 3 chicks and the 3 banties in about 2 weeks. I will keep her separated where she is for a week or 2. Then I will try freeranging her back into the flock. Last year I didn't have things separated the way I do this year, and when I tried to integrate, it was always with her chicks, even when they were six months old, and she was still protecting them. She was my only banty, and some of my standard hens would take her right down.
I like that broody raised chicks are smarter, but I so much more enjoy the chicks that I raise!