The question shouldn't be "is pie chart X better than bar chart Y for making point Z?" but "what is the best way to express point Z?"

In this case, the given bar chart was a poorer way to express the point. Here's a text diagram which I believe is more informative than the give pie chart, though I have some fencepost errors due to character alignment.

    [      A    │  B │ C │D]
   0'     '     '12   '    '24

A variation is:

    AAAAAAAAAAAABBBBBCCCCDDD
   0|     '     ½    '     |1

or if you don't want to count the letters, here's a variation with an explicit count:

          A       B    C  D
    [----12----][-5-][4-][3]
   0|     '     '    '     |24

This is a fair, if terse, summary. However it should be more explicit with the practice accepted as potentially the most evil use of pie charts: any comparison between two, or more, pie charts where the whole has also changed in some fashion. This is most commonly seen as some breakdown of budgetary expenses compared between two years where the total budget has also changed. Attempting to depict this additional change by making one pie larger doesn't work as the eye is too easily fooled between angles and areas. So unless you can somehow assure the audience that the two pies have the exact same base don't compare pie charts.