Brown rice has more fiber. White rice also is enriched by law in the US,
so your comparison is not really fair.
But the amount of fiber in a cup of beans pretty much dwarfs the amount you
are going to find in rice, anyways.

I eat both kinds of rice. Medium-grain brown rice is harder to get
sometimes, so I'll either eat short-grain brown from the health food store,
or medium-grain white rice I pick up in the Hispanic section (Goya, for
instance). Long grain rice is just not authentic for many kinds of food.