This outer layer of bran means that brown rice takes longer to cook than ordinary rice. See How to Cook Brown Rice.
Brown rice has a slightly nutty flavor and a firmer texture than regular rice. Because the bran provides dietary fiber and essential fatty acids, and the germ contains a number of nutrients, brown rice is generally considered healthier than ordinary white rice.
Indeed, it is to make up for the relative lack of nutrients that white rice is typically enriched with vitamins B1, B3 and iron. Even so, brown rice provides nearly four times the protein as white rice, and there's no way of adding this protein back into the white rice.
The fatty acids found in the rice bran can eventually turn rancid and spoil. Thus, brown rice has somewhat of a shorter shelf-life than plain white rice.