You should add "both" as an option, as a lot of folks seem to do a combination of both.
This is all personal preference, and I guess it depends on how involved you want to be, or what the purpose of the chicks is. Incubator-raised and indoor-brooded chicks are more tame and human-friendly. This year I let a broody hatch chicks just to get the experience of having a mama with babies, which I thought would be cool for my kids to experience. A friend of mine gave me the eggs to hatch for her, and she'll be taking the chicks back after mom weans them, so tameness is not as important in this case. However, I also hatched chicks for my family in an incubator and am brooding them in the house, because I want those chicks to be tame and to let my kids handle them and play with them. If I were to keep pet chickens, I would not let a broody hatch them. They need maximum exposure to humans as early as possible. However, I am considering raising some extra chickens for meat next year, and those I can let a broody hatch and raise for me since they don't need to be as tame.