I think in terms of space and efficiency, battery cages win out because you can squeeze significantly more chickens in a given area. Eggs from caged birds were probably cheapest just due to sheer volume of chickens in a given area.

Cage free still isn't perfect though. The chickens are still pretty crowded and practices like beak trimming and forced molting are still used on some farms. At the same time, free roaming chickens can easily get sick or injured from fighting each other (chickens are dicks who love to fight) or spreading disease through feces. So trying to balance out health and efficiency is still an issue. I think we're taking a step in the right direction and while I'm not a fan of raising food prices, I think the majority of people can swallow an extra nickel or two per egg if it means they come from a better source.

Wired has another good article about the transition to cage free, listing some of the difficulties the food industry is facing.

Another shout out to kantos here, because the Wired article is also informative in a different way.