You might want to reread the article in my signature. It's not copyrighted so feel free to use anything in it. You don't need to give credit, it's out for the general public.
The three general things I normally mention are that I get fewer behavioral problems, don't have to work as hard, and have more flexibility to deal with problems that show up if I have more room.
An example of behavioral problems. A typical way chickens resolve conflict is the weaker runs away and avoids contact with the stronger. If they don't have room to get away or avoid to start with what would otherwise be a minor skirmish can turn into a serious fight. That's more avoiding problems.
Maybe broody hens raising chicks fall into this. My problem is not so much that Mama can't take care of her chicks if it is a bit tight, though mine tend to keep their chicks separated when the chicks are young. My issues are more after Mama weans them and leaves them alone to make their way with the flock. They no longer have Mama's protection so have to rely on themselves to avoid the adults and get away. Mama may have spent a few weeks teaching the other chickens to leave her babies alone but after they are weaned if they invade another hen's personal space it can get nasty. You can get the same a effect with brooder-raised chicks. The look but don't touch may get the adults used to them but the more room they have to avoid the adults the easier it usually is.
The work as hard usually comes to poop management. The tighter they are the more they poop in a small area so the poop builds up fast. That's already been discussed some.
Flexibility is my favorite. Say you need to isolate a chicken in a predator proof area. Could be an injured chicken or maybe two are fighting. If you have room in your coop you can set a crate in there or build a quick shelter. If your coop isn't that big you can't do it. Say a predator starts picking off a chicken a day. If you free range your coop/run needs to be big enough you can protect them in there while you deal with the predator or leave them locked in there for a few weeks and the predator moves on. I've done that. Or you have a predator getting into your run or you just need to lock your chickens in the coop only while dealing with the run. Is your coop big enough to do that? If you wake up to a problem can you lock them somewhere so you can deal with it after you get home from work instead of taking a day off? Say you need a broody buster, can you rig one up in a predator safe area? If you are integrating juveniles do you have room to put in a juvenile roost so they don't sleep in your nests?
Hopefully you can get something out of this that you can use. And give a link to that article when you finish it. If you want someone to proof read it let me know.