Laying would probably be the easiest provided they are doing it on their terms, such as without supplemental light and so on. That is because laying an egg is just another menstrual cycle for them and is perfectly normal.
Second would be moulting. They have a hormonal change, drop their feathers and expend energy to grow them back. Given a proper diet enriched with some healthy treats with extra protein, it shouldn't be that stressful as they have the nutrients to get feathers back. They'll just have to eat more, spend more time grooming, and be a bit cold if it is the winter.
Brooding is BY FAR the MOST stressful on the hen. It is a HUGE hormonal change that makes the birds sit on a nest 24/7. She will eat one time a day, go potty one time a day, and sit on that nest for her life. She will no go to roost, will neglect to take baths and clean her self up, all to hatch eggs if the mood is right. There are cases where hens have died sitting on a nest because they did not get up to eat or drink. A broody who has sat on eggs for just 3 weeks will lose a lot of body weight. My best broody hen loses 1-2 lbs during her broody cycle, which is alot for a 6 or so lb hen. Often they can become skin and bones while setting. Furthermore, they will often protect that nest for their lives and often won't leave the eggs even if death comes sniffing them out for a meal. Every disturbance to the nest, even other hens coming by, stresses them out in their mind set.
Now for scientific proof, since these factors aren't really studied in production animals, I don't know of any articles that exist to show these traits, since laying more eggs, force molting, and artificial incubation are the main goals that are funded. The above ideas are just observations with some reasoning.
