Graphene-based detectors of THz radiation – despite their improvement over the years – continue to exhibit a lower sensitivity than detectors made from other material systems. In order to gain a deeper understanding of some of the detection processes and their constraints, we analyze here experimentally and by simulations the operation of graphene TeraFETs, detectors based on rectification in antenna-coupled field effect transistors, over the frequency range 0.1-1.2 THz. The devices were fabricated with an advanced wafer-scale process technology. It is well-known that two detection mechanisms contribute, resistive self-mixing and the photothermoelectric effect. We determine the respective contributions to the responsivity and their frequency dependencies, put the results into perspective with competing technologies, and suggest ways to improve detector performance.