There's at least one nutritional advantage you can gain by using whole milk that is from cows in an organically-certified dairy. "In the first large-scale study to compare milk from organic and conventional dairies across the United States, the researchers found significantly higher levels of heart-healthy fatty acids in organic milk.
The reason is that organically raised cows eat more grass and less corn and other grain-based feed than their conventional counterparts, said lead author Charles Benbrook, of Washington State University’s Center for Sustaining Agriculture and Natural Resources."
You can read a nice summary by Sandi Doughton of The Seattle Times. You can also read the original research. And there's a variety of information available from Washington State.