That is a really good question. (I've stepped away and come back to my computer so hopefully I'm not at the end of a long line of answers for you here).
In my opinion, the answer will be different for each chicken owner and totally depends on your chicken philosophy, flock needs, and goals. How much property and your physical environment will also determine which is better as well as how long you actually want to keep chickens.
I have done it both ways and have transitioned over the years to using only broodies.
If you are in the chicken business for profit, your needs will be different than the average backyard owner.
If you want to sell chicks for profit, especially of expensive breeds, then you likely want the ability to brood whenever you want, no matter the season, and will want to be able to carefully control all aspects of hatching and grow out. You'll want a very good incubator and industrial quality process. (Although @PD-Riverman who has perfected the use of broodies for more of a business set up.)
If your focus is layers for an egg business (like my grandmother was), you'll likely just buy a new set of chicks each spring and brood in a separate building with heat lamps...no guesswork as to how many live chicks you get. Let the hatchery undertake the cost and effort of bad hatches.
If this is a hobby, or you are wanting to keep a sustainable flock on a bit of land, I can highly recommend hen brooding. Once you understand the mechanics and set up, hen brooding is very efficient.
I have read several studies (done in 3rd world Agricultural studies) that show broody hens can be 80 to 90% efficient in obtaining a clutch. Most inexpensive incubators are about 50%. Better quality incubators, with a knowledgeable handler, can come to almost 100%, but average around 80%. See our own BYC @PD-Riverman for his personal best (overall) percentage.
I personally am lousy at hatching with incubators (did a bit of that with a 4H project with my kids). Mostly because I never would dole out the dollars to get a good one. The cheap incubators are a lot of work and require a lot of fiddling to get good hatches. However, I was reluctant to get a good one because I discovered I really didn't like the mess and hassle of artificial brooding chicks with a heat lamp inside the garage. (Over time, the mess gets really, really old.)
While we were pondering that decision of how to best brood with our start up flock, a huge turning point came when we burned a coop down to the ground, to ash heap, by adding a flood lamp to keep the newly transitioned pullets (from the artificial brooder) warmer during a really big cold snap. Turns out most of our chicken friends had either had a fire or nearly had a fire from heat lamps. The fire was so intense that it scorched the nearest tree but thankfully missed our wood pile and the neighbors. I could have easily burned down a whole area on the map.
So that set a bad taste in my mouth for heat lamp brooding, especially in the garage. I decided to set up to brood the natural way and have never looked back.
During that transition year, I even had artificially brooding chicks along side naturally brooding chicks.
I can honestly tell you that the naturally brooded chicks grew faster, feathered quicker, were overall healthier, and had no transition issues or losses. No pasty butt, no coccidiosis, and absolutely no need for artificial heating even in the dead of winter. Momma literally does all the work, and you have healthy little babies running around with snow on the ground. Those winter hatches generally mature early (as they mature during lengthening day light) into pullets that lay early.
This is offset with less efficiency on hen brooding than at top rate artificial incubator/brooder. (I overall get maybe 66% to 70% hatch rates...but I am dealing with a couple of less than satisfactory bantams which has lowered my rates...my good broody hens are at about 90 to 100% hatch rate consistently....survival rate is nearly 100% though...lost one in winter who wandered out of the grow out pen.)
Broody hens will only brood when they want to, while an incubator is ready to fire up at will. You can increase your frequency by purchasing known broody hens or pullets from a really good brooding line and breed. My Silkies have gone broody at least 3 to 4 times a season. My bantam Cochins likewise...although somehow their fluff is not as effective as a Silkie. My breeder quality heritage Marans and Rhodebars are probably twice a year.
The hen brooded chicks are not as tame as artificially brooded chicks, if you were to handle them a lot, but they are wonderfully adapted to being chickens and living smartly on free range.
So there are pros and cons of each method. Choose the method that best fits your needs and goals.
LofMc
