Comparison and contrast of two general functional regression modelling frameworks

In their article, Greven and Scheipl describe an impressively general framework for performing functional regression that builds upon the generalized additive modelling framework. Over the past number of years, my collaborators and I have also been developing a general framework for functional regression, functional mixed models, which shares many similarities with this framework, but has many differences as well. In this discussion, I compare and contrast these two frameworks, to hopefully illuminate characteristics of each, highlighting their respective strengths and weaknesses, and providing recommendations regarding the settings in which each approach might be preferable.