When do I have to use aucPR instead of auROC? (and vice versa)
Yes, you are correct that the dominant difference between the area under the curve of a receiver operator characteristic curve (ROC-AUC) and the area under the curve of a Precision-Recall curve (PR-AUC) lies in its tractability for unbalanced classes.  They are very similar and have been shown to contain essentially the same information, however PR curves are slightly more finicky, but a well drawn curve gives a more complete picture.  The issue with PR-AUC is that its difficult to interpolate between points in the PR curve and thus numerical integration to achieve an area under the curve becomes more difficult.

Check out this discussion of the differences and similarities.

Quoting Davis' 2006 abstract:


  Receiver Operator Characteristic (ROC)
  curves are commonly used to present results
  for binary decision problems in machine
  learning. However, when dealing
  with highly skewed datasets, Precision-Recall
  (PR) curves give a more informative picture
  of an algorithm’s performance. We show that
  a deep connection exists between ROC space
  and PR space, such that a curve dominates
  in ROC space if and only if it dominates
  in PR space. A corollary is the notion of
  an achievable PR curve, which has properties
  much like the convex hull in ROC space;
  we show an efficient algorithm for computing
  this curve. Finally, we also note differences
  in the two types of curves are significant for
  algorithm design. For example, in PR space
  it is incorrect to linearly interpolate between
  points. Furthermore, algorithms that optimize
  the area under the ROC curve are not
  guaranteed to optimize the area under the
  PR curve.


This was also discussed on Kaggle recently.

There is also some useful discussion on Cross Validated.