The most prominent formal criterion for secure compilation is full abstraction, the preservation and reflection of contextual equivalence. Recent work introduced robust compilation, defined as the preservation of robust satisfaction of hyperproperties, i.e., their satisfaction against arbitrary attackers. In this extended abstract we provide a high-level presentation of our findings in comparing these two approaches to secure compilation. Our goal is to make our results accessible to an audience interested in formal methods for secure compilation, but non necessarily familiar with some of the required background from category theory.