Both methods have pros and cons.
Broody hens may seem easier, but when it comes to the actual incubation process, it's really just as time consuming as an incubator. First, you will need to have a hen go broody. This is just a matter of having a broody breed and waiting. Hens may not brood when you want, in fact they will likely brood at the exact opposite time. However, if the bird has the instinct to brood, she eventually will. Once she has done that, you will need to separate her to her own area with feed and water. After that, just give her some eggs and wait. She will hatch them out and the hen and chicks can be reintroduced to the flock at 8-10 weeks of age. Mind - these are living creatures, so they are subject to their own quirks and whims. Some hens may not be good mothers.
An incubator, of course, is more controllable. You decide when to brood, and can control the exact factors of the incubation environment. A good starter incubator (I'm talking a proper forced air machine here, not a styro-crap-bator) will probably cost you a good investment of $150-$300, but it will also last you years and give you good hatches. In a single season, I've hatched 100+ chicks out of a $150 incubator. If I continue to use it yearly, and it lasts at least, for example, 5 more years, I could produce 500+ chicks - a good return on an investment of $150. Obviously, not everyone WANTS to produce that many chicks, but in any case it's a testament to the usefulness of these machines. Aside from the investment, many incubators are set it and forget it - most machines fully control temperature and turning, and digitally controllable humidity is somewhat common as well. Also - an incubator can't crush or kill your chicks.
Everyone will have their own opinions on this subject. Personally I prefer incubators, as I have maximum control of the incubation and hatching process. I do have one hen I allow to brood, but even her I do not give my important eggs - she gets dual purpose mutt babies to raise.
