Howdy
nyrunner
I have only had hatches with a broody hen and do not own an incubator so cannot really comment on both sides of the scale but some of my thoughts are:
A broody hen does all the work … pretty much set and forget. No issues with temperature spikes, humidity etc; no egg turning [some incubators will do that for you].
When the chicks hatch, no need for a brooder [unless she is a bad mumma]; she will raise, educate and protect them.
There is a chance your broody, if a newbie to the whole hatching thing, might leave the nest but then your incubator could fail also.
There is also the chance that, if left in the coop with the rest of the flock, eggs could get damaged which is probably not going to happen in an incubator.
A broody hen on the nest is an open invitation for lice and/or mites as she is a nice, constant source of food and warmth and again, not going to happen in an incubator.
With an incubator you can see pipping, zipping, hatching etc .. dependent on the broody, you might not get to see the little ones until they are a couple of days old
With a broody hen you are limited to the number of eggs you can put under her .. depending on the size or number of incubators, you can set however many eggs your heart desires.
A broody hen can lose weight and condition while on the nest .. an incubator will not
You can turn an incubator to ‘On’ .. you cannot turn a hen to ‘Broody’