Brown Rice and White Rice have approximately the same amount of carb per serving (1/4 cup). (My database shows 34g of carb in Brown VS 36g of carb in White) The key differences between brown rice and white rice is that brown rice has more fiber and it also has a much lower G.I. (Glycemic Index)
You might ask, why is low GI better than high GI? Low GI carb source will less likely induce insulin spilke upon consumption. Insulin spike promotes fat storage. (turn carb into fat and store it for later use)
Is low GI carb ALWAYS better than high GI carb source? The answer is NO. After intense weight training, it is always a good idea to consume high GI carb (i.e. Dextrose, Maltodextrin) because your body is prime for nutrition absorptions (and also low in blood glucose after workout)
Hope that helps.