Technically, all digital camera are B&W cameras. They use filters over the sensors in an array so that each sensor picks up only the blue, red, or green wavelengths. The camera's software knows which filter is located over which pixel, and reconstructs the color image from this. Often, they'll use a bayer array, where each pixel represented on a computer screen is made from four pixels on the sensor 2 green, one red, and one blue.
So the advantage of using a B&W only digital camera is you can get 4x's as many pixels out of the same sensor, since you're not having to dedicate 4 sensor pixels to each computer screen pixel. You can use a 1:1 ratio. This also allows you to use larger sensor pixels which will often have more sensitivity. And since you don't have the colored filters over each pixel, they can gather more light.
So if B&W photography is your only concern, it makes sense to buy a B&W digital camera. Though for most of us, it's probably not worth the expense, seeing as how easy it is to turn a color digital camera into a black and white image.