i keep chickens both ways, and i can tell you that it takes alot more work to keep chickens in small pens. feed has to be adjusted to match for lack of insects and greens if the cage is to small, or they cant get to it.
i know 10 square feet of outdoor run space is generally accepted as the right amount of space. i really think it should be more, perhaps 50-75 square feet per chicken so the grass doesn't wear down as fast. of course if you free range during the day, you wouldnt need as much space in the run.
this is just one of those questions that is impossible to answer completely. everyone has different situations, nutrition, and even plants and insects. 10 chickens can work over an acre a day in a free range application.
ok, now to the smallest area. in my breeder's pens i can keep 3 large fowl (white rocks, silver laced wyandottes, etc) in a 3x4 pen. these chickens dont have outside run access, so feed and care becomes alot more intense. we have to lower the fat, and add in "green" items to take the place of grass. we use dried mealworms and (fresh) nightcrawlers to aid in protein. since there isnt alot of room for dustbathing, we have to constantly monitor for lice and mites. waterers are on the outside of the cages to help keep them dry. when we aren't using the chickens for breeding we do let them outside in tractors, for exercise. the tractors are 8x8 feet. and tarp covered to prevent hawk attacks. i do not recommend this system to someone who just raises a few birds for egg purposes. when you get into rare breeds that costs hundreds of dollars for a baby chick, you become alot more cautious. for these people (if they are interested in breeding) this system will work well, but with a flock of (we will say) over 200, you will find it hard to work a full time job and take proper care of your chickens.