It looks like it is not a new study but rather a meta-analysis of existing studies: "Demand for organic foods is partially driven by consumers’ perceptions that they are more nutritious. However, scientific opinion is divided on whether there are significant nutritional differences between organic and non-organic foods, and two recent reviews have concluded that there are no differences. In the present study, we carr…
Their top claim seems to be that organic food is higher in anti-oxidants. Unfortunately, the idea that anti-oxidants are good for you has always been scientifically shaky, and as more studies have been done, it's increasingly looking like anti-oxidants may be unhealthy. So, the message of this study is, avoid organic food?
The combination of studies shows not that "antioxidants are bad" but that we don't understand how to isolate their benefits. Diets high in antioxidants from whole foods (dead plants and animals), rather than nutraceuticals or supplements, are consistently linked with health. Apparently it's not so simple as isolating one compound -- we need a balance of chemical compounds coming in, working in concert.
(It's like we evolved to thrive on real food instead of pills! Weird!)