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
This was also discussed on Kaggle recently.
There is also some useful discussion on Cross Validated.