Depends on the food-- Organic Tomatoes have more Vitamin C
A large review in 2006 showed that different vegetables have different contents depending on the farming practices used (ie, organic vs non-organic). Most helpful here, including sources, is Table 2 of that study. In that table, the following statements describe the results of various fruits and vegetables, as well as providing references to each claim:
So, as the chart shows, organic tomatoes have more vitamin C.
The recent claim, as reported by the NYT and NPR, glosses over these levels of minute variation. Note also, that the Stanford study, linked by @vartec and the foundation of the NPR article, discusses health effects in humans, not vitamin content in the fruits themselves.
The conclusions of that review did mirror those of the Standford study, notably:
This review illustrates that tradeoffs exist between organic and conventional food production. Organic fruits and vegetables rely upon far fewer pesticides than do conventional fruits and vegetables, which results in fewer pesticide residues, but may also stimulate the production of naturally occurring toxins if organic crops are subject to increased pest pressures from insects, weeds, or plant diseases. Because organic fruits and vegetables do not use pesticides or synthetic fertilizers, they have more biochemical energy to synthesize beneficial secondary plant metabolites such as polyphenolic antioxidants as well as naturally occurring toxins. In some cases, food animals produced organically have the potential to possess higher rates of bacterial contamination than those produced conventionally since organic production generally prohibits antibiotic use. The prohibition of antimicrobial agents also explains the apparent lower incidence of antimicrobial resistance in bacterial isolates of organic food animals, as some studies have shown a correlation between increased rates of antibiotic use and increased antimicrobial resistance.
So, organic tomatoes have more vitamins, the tradeoffs for producing and eating them may not be good.
Also, it's important to note that the review referenced in @ilvel's answer mimics the results of the 2006 study I posted, namely:
In this chart, note that there is a difference between organic and nonorganic foods as relates to vitamin C concentration.