Is there a functional difference between black and white Wii remotes?
There is no difference except for the colour.
I'm not familiar with the actual prices, but one thing to pay attention to is whether or not you're looking at a normal Wii Remote or the Wii Remote Plus that includes the MotionPlus sensor. If that's not it, then the price difference you're seeing is simply due to the "novelty" of the black controller.
There's no difference. It's the same thing except one is black and the other one is white. The black Wiimote is newer than the white one. Other than that, it's the same thing.