So if you are vegetarian for environmental reasons and had to eat a chicken, you should go with the battery-farmed one.
You would go with the (arguably mythical) happy chicken if you were vegetarian for moral reasons.
> feed (less energy expended from movement)
Less muscles, more disease, worse health, lifespan of 4 weeks, &c.
Given the same amount of money, I'm assuming they mean buy less chicken (but from non-factory sources) and spend the remainder on other foods with less environmental impact.
They're free to move about at least in their "bay" and have the company of other hens that can wander about too. Sure, they don't get the marketing feelgood "sun on their backs and wind in their feathers", but they also don't get raptors, foxes, or rats.
You can get rescue hens and they're just about savvy enough to figure out - after you've lost one or two - that predators are a thing, and you'll get an egg every couple of days per hen. They'll eat all the bugs in your garden (and most of the herbs, and the tops of your carrots) and shit everywhere.