GaAs nanowires are promising candidates for advanced optoelectronic devices, despite their high surface recombination velocity and large surface-area-to-volume ratio, which renders them problematic for applications that require efficient charge collection and long charge-carrier lifetimes. Overcoating a bare GaAs nanowire core with an optimized larger-bandgap AlGaAs shell, followed by a capping layer of GaAs to prevent oxidation, has proven an effective way to passivate the nanowire surface and thereby improve electrical properties for enhanced device performance. However, it is difficult to quantify and distinguish the contributions between the nanowire core and cap layer when measuring the optoelectronic properties of a nanowire device. Here, we investigated the photoconductive terahertz (THz) response characteristics of single GaAs/AlGaAs/GaAs core-shell-cap nanowire detectors designed for THz time-domain spectroscopy. We present a detailed study of the contributions of the GaAs cap layer and GaAs core on the ultrafast optoelectronic performance of the detector. We show that both the GaAs cap and core contribute to the photoconductive signal in proportion to their relative volume in the nanowire. By increasing the cap volume ratio to above 90% of the total GaAs volume, a quasi-direct-sampling type photoconductive nanowire detector can be achieved that is highly desirable for low-noise and fast data acquisition detection.