Ironically, the basic fact is that neither GR nor QM are usually needed on a daily basis for most astronomers. Only a cosmologist or black-hole astrophysicist will need GR daily, and only a spectroscopist or white dwarf modeler will need QM daily. However, these are the two main theories for explaining what is happening everywhere, so they will underpin everything else. So I think it depends on how deeply the astronomer wants to feel their results are anchored into the foundations of physics as to whether or not they regard GR or QM as important at all, not to mention which one is more important. With that in mind, QM is more fundamental, because it is involved in every single astronomy observation, it is just a matter of whether or not the astronomer cares about that fundamental connection in practice. In that same vein, it would be virtually impossible to obtain a PhD in astronomy without several courses in QM, but you can do it with quite little GR if you navigate your course that way.