In this work, we compare the photodetector performance of single nearly defect-free undoped and n-i-n GaN nanowires (NWs). Undoped NWs present a dark current three orders of magnitude lower than n-i-n structures, about ten times lower gain, and a strong dependence of the measurement environment. In vacuum, undoped NWs react with an increase of their responsivity, accompanied by stronger nonlinearities and persistent photoconductivity effects. This behavior is attributed to the unpinned Fermi level at the m-plane NW sidewalls, which enhances the role of surface states in the photodetection dynamics. In the air, adsorbed oxygen accelerates the carrier dynamics at the price of reducing the photoresponse. In contrast, in n-i-n NWs, the Fermi level pinning at the contact regions limits the photoinduced sweep of the surface band bending, hence reducing the environment sensitivity and preventing persistent effects even in vacuum.