I have not encountered many box and whisker plots or histograms during my MPH.
I think they are easy to understand, but I think the histograms are a little easier than the box and whisker plots.
I like how the box and whisker plots show the outliers in the data set, and I think for a data set with more variance they are useful.
For alternatives, I would use a bar graph to represent the data. I think it looks similar to a histogram in how it distributes the data. They both convey the shape of the data well.