I usually do 2 runs of 30 eggs each in the incubator and one run with a broody per year - this is my experience only - as the americans say: YMMV.
Broodies do all the work for you from the incubating to the nurturing keeping them warm and safe and showing then where to eat. However they can be unreliable, they can sit for almost the full time then suddenly decide they are bored with the whole business. I've also had one that attacked her chicks once they were born - pretty unusual behaviour though. And of course that won't be laying eggs for a good couple of months. The hens (and cocks) raised by a broody tend to be more streetwise than those artificially raised.
The advantages for the incubator method are about timing - you know when they are coming and how many you are likely to get (assuming you have a reliable source for your fertile eggs). However you have to be look after them yourself with heat lamp or electric hen for up to 8 weeks or so depending on the time of year. You could have a go at hatching eggs at almost any time - it works commercially, but for us home breeders the usual sources are very seasonal and certainly my cockerel is not very active currently I expect fertility would be very low.
There's plusses and minuses to both methods and you can't beat the sight of the mother leading her chicks around the garden
BUT make sure you have a plan for the boys - rehoming is very difficult unless you have a properly rare breed - Don't assume someone will take them off your hands (except for the pot maybe) Personally I grow mine on until they get started on the crowing then I despatch them, skin them and boil them up before stripping the carcasses and freezing for a source of chicken meat for curries, pasta etc (they don't roast well)
Good luck with whatever you decide - raising chicks is lovely whichever way you go.