For a more objective analysis, simply compare the nutrition data on the labels of minute rice versus regular rice. Compare equal quantities of cooked rice. If you don't want to stand next to the grocery shelves with a calculator in hand, you can check the food nutrient database maintaned at www.usda.gov. They probably have multiple variations of rice in their database and you can get data on equal serving sizes for comparison.

Obviously brown rice has more nutrients than white rice since you make white rice by starting with brown rice and stripping away the outer layer. Although white rice is typically enriched to add back some of the nutrients, it's unlikely to fully compensate. Note that for maximum nutrition you should not rinse white rice before cooking.