Everyone knows the only reliable source for science on the internet is Natural News.

That the nutrition would be the same just without a side of pesticide and chemicals.

It's about less health risk from pesticides, injected hormones, antibiotics, etc., lower ecological burden and risk, and striving to match output without input-intensive agriculture (density through complementary crops and attempt at permaculture). Anyway, "organic" labeling is a joke and organic is still at least as much aspirational as actual. Regional sourcing (reduced transport) needs to be as much a consideration in a truly ecological system as any other factor.

It just has less pesticides and antibiotics

which is a typical RW tactic. Debunk a claim we never made in order to discredit the whole idea. If they sell the uninformed masses on the idea that there is no difference between organic foods and non-organic foods, they can reduce demand for organic foods and up the sales of factor farm created and GMO-laced whatever. So the study was a boon to the factory farm industry.

NPR got so many complaints about the story they had to go back the second day and explain that the claim that was "debunked" was a claim that nobody was making and to explain that the study neglected to look at environmental effects.

Here's a claim from the first web site that I found when searching for the Advantage of Organic Farming. It happened to be from an Australian site:

The nutritional value of food is largely a function of its vitamin and mineral content. In this regard, organically grown food is dramatically superior in mineral content to that grown by modern conventional methods. advantages and disadvantages organic farming

Because it fosters the life of the soil organic farming reaps the benefits soil life offers in greatly facilitated plant access to soil nutrients.

The study may have only looked at vitamins, not minerals. It may have only looked at the most common macro-nutrients, not micro-nutrients. It may have taken its food samples from farms that were recently converted to organic and had not restored the full balance of nutrients in the soil.