Under digital, it doesn't make sense to capture the data in black and white; that is to say, to shoot that way.
With film, it is usually a decision about how to capture the picture: you can use black and white film, and shoot in black and white. Yet, not necessarily. A color negative can be processed to black and white paper. Because that's not the same thing (black and white film has its own behaviors and nuances), there is a case to be made for shooting black and white: a certain type of film captures an image in a way that only that type of film can capture, and that is part of the art.
Since a digital camera has a color image sensor, if it allows black and white shooting, that's because software on the camera reduces the RGB image data to grayscale. It's probably better to shoot in color and then have control over the algorithm for doing this conversion, rather than leaving it in the hands of the camera firmware, unless it documents how it is done.
Converting to black and white is a tricky business. The main question is: which color model is used to determine the lightness of a pixel? For instance, we can convert RGB pixel values to the HSV color space, and then just take the V channel as a grayscale image. But this is not accurate. A pure, saturated blue color (
#0000FF, in a common RGB notation) is darker than a pure red (
#FF0000). Yet, the V value under HSV is the same. If the conversion to grayscale is based on the V from HSV, color will affect lightness in a way which is incorrect with regard to human perception.
A good way to convert to grayscale is to map the image to the LAB color space, and take the lightness channel as the source for the grayscale data. Not literally of course, because the L channel is logarithmic; rather, the A and B channels get obliterated to gray, and then the LAB values are recomposed to RGB. The LAB color space takes into account differences in brightness among the colors: the L channel is normalized accordingly.
If I cared about producing great B&W images, I would only rely on the camera if I was sure it was doing the conversion in a way that handles the perceived lightness of colors properly: either by using this LAB color space, or else, say, based on some function which emulates the behavior of black and white film (how its lightness is influenced by color).