We systematically explore the interaction of an AFM tip with single CdSe/CdS quantum dots and seeded CdSe/CdS nanorods. Using distance-dependent intensity and lifetime near-field microscopy in 3D, we analyze the interplay between quenching and enhancement in proximity to the tip. Under tightly focused radially polarized excitation, a nanoscale, central enhancement spot is observed for both types of particles, revealing an identical physical mechanism underlying the near-field interaction in both cases. Furthermore, lifetime and intensity near-field images of both types of nanoparticles exhibit characteristics similar to those of a single molecule with a well-defined molecular dipole. We also investigate the origin of the observed enhancement effect. By exploring the dependence on excitation polarization and tip material, we conclude that the main contribution to the fluorescence enhancement is from excitation field enhancement at the apex of the tip, serving as a lightening rod. However, we also show clear correlation between the particle quantum yield and the measured enhancement factor, providing a direct proof to a limited contribution of emission enhancement as well.