HDIFFB treats the histogram bins individually, while HDIFF treats the histogram as a whole. In HDIFF, one is comparing the overall shapes of a probability distribution. Typically, an event is entered only in one channel, and the choice of channel depends on a measured value of a continuous coordinate, so that it makes sense for downward fluctuations in one bin to be considered as compensated by upward fluctuations in another bin. In HDIFFB, each bin is considered independently, except, perhaps, for an overall normalization factor which is the sum over all bins.
Thus HDIFFB is appropriate when:
A plot of hits versus detector element, where the detector elements cover some angular range, is an example of a histogram which might be considered with either comparison utility. The choice depends on the question you wish to answer: