Pros and cons of low-power integrated series voltage regulators vs. shunt regulators
To me the critical difference is how they handle loads with varying power requirements. 

A shunt regulator will always take the same power from the supply, even if the current drawn by the load is reduced. In some scenarios this could be a positive feature.

A series regulator will take less power from the supply if the load current drops. In some scenarios this could be a positive feature. This also makes the series regulator more tolerant of sloppy design --- you don't have to know exactly the maximum and minimum power that might be needed by the load in order to design with the series regulator, and your design is not penalized (with extra heat generation) if you overestimate the load's current requirement.