Free range chickens get more exercise. This is healthier for the chicken, developing more muscle and cutting back the fat. Theoretically, this lowers cholesterol and if the chicken is healthier, so would its eggs... I personally prefer the smaller eggs. I grew up on a farm, and never saw natural chickens produce jumbo eggs.

Free range is better as the hens are fed on better diets and are healthier in general. They aren't cooped up as much as factory farmed hens which results in better quality eggs. There is some research which suggests that they contain higher levels of nutrients (mens health mag i nicked off boyfriend!) I aways buy free range as i cant bear the thought of helping to sustain the market of factory farming for animal cruelty reasons.

Free range eggs are better for your soul! You know where they are coming from. We all need to work together to ban the production of caged eggs from battery hens! 

Personally, I think they taste so much better! There is no gamey taste!

(As a vegan for 7 years, I now find it difficult to eat factory farmed eggs.)

 

But to more directly answer your question, there is no significant nutritional difference according to a Time Health article from July of 2010:

Organic Eggs: More Expensive, but No Healthier

"The Haugh unit factors together the weight of the egg and the thickness of the albumen layer at the center," says Jones. And that number, she found in her study, is not affected a whit by how a hen is raised. "We found no meaningful differences at all," she says. "We sampled eggs from a number of stores and kept getting the same results over and over. For shoppers, the decision comes down to your ethical and moral choices."