I personally vote incubation. However much I love to watch a broody hen with her chicks out on the grass in the Spring time, I've found I've had a lot of trouble with broody hens.
Lots of my broodies have sat for 3 weeks, but when the chicks hatch, they kill them intentionally (which is horrid). Even if the hens don't intentionally kill the chicks, I constantly worry that she'll crush them with her feet, as I've had that happen several times.
My experience with Broodies hasn't been great, here are three of them:
1) The hen sits perfectly for the first to weeks. Then literally THREE days before they're due, I go out there and find the hen away from the nest, and the eggs stone cold.
If I'd had them in an incubator, this wouldn't have happened.
2) The hen sits on 4 eggs happily for 3 weeks. I go out on day 21 and find two totally squashed chicks, still not completely out of the eggs.
If I'd had them in an incubator, they would never have been crushed.
3) Three perfect fluffy chicks hatch on day 21. Mother is perfect with chicks and everything seems fine. The next morning I go out and find ALL THREE dead next to the slightly raised nest.
If I'd had them in an Incubator, they couldn't fall out.
This is just my experience. I've heard people have great luck with broodies and it works perfectly, but I find an incubator is better for me. Sure, there is the risk of power cuts that you don't get with a hen, but overall, the incubator is less risky.
-Jet