I have not seen any study of that sort. But one way or another any investigation on this regard will need to have nutritional analysis of the two types of chicken which likely will be influenced by the location and farming conditions. Is this a personal interest question or are you a researcher or student trying to study the subject?. It is not clear what is your background or research interest 

Assuming your interest was about the long-term impact of organic or free-range chicken (or more broadly, poultry) consumption on health outcomes, unfortunately, to my best knowledge, there is a lack of such data in the scientific literature. 

However, there are some articles about the consumer perception or attitudes towards consumption of organic poultry:

1. Psychographic, demographic and economic factors associated with organic poultry consumption: http://agris.fao.org/agris-search/search.do?recordID=US9040440

2. Qualitative attributes and consumer perception of organic and free-range poultry meat: https://www.cambridge.org/core/journals/world-s-poultry-science-journal/article/div-classtitlequalitative-attributes-and-consumer-perception-of-organic-and-free-range-poultry-meatdiv/C17F5D0B7D747DC2578B1B0672F4DFEE

3. Effect of Organic Poultry Purchase Frequency on Consumer Attitudes Toward Organic Poultry Meat: http://onlinelibrary.wiley.com/doi/10.1111/j.1750-3841.2010.01775.x/full

At the best of my knowledge there aren't papers on the effect of eating organic chickens. Moreover. I don't understand how such type of studies could be managed. There are a lot of confunding factors starting from the meat quality (it is affected by strain, pasture and feed) to the composition of human diet etc.....