A new type of pyropheophorbide-fullerene [60] dyad was synthesized by their attachment by the cyclopropane backbone at the 13(1)-position of the chlorin macrocycle using the Hummelen-Wudl method. Here we report a complex analysis of the structure influence on the photophysical properties of the newly obtained dyad and its comparison with another pyropheophorbide-fullerene [60] dyad. The latter dyad was previously obtained by the attachment of the tetrahydropyrrole backbone at the third position of the macrocycle using the Prato reaction. It was shown by quantum-chemical modeling that the studied dyads have drastically different spatial positions of the fullerene core relative to the dye macrocycle plane: "parallel" for the former and "perpendicular" -for the latter. The influence of structural differences on various properties of dyads was studied: the aggregation properties, absorption spectra, the fluorescence quenching of the dye moiety in the dyads, and the lifetimes of excited states. The data obtained are important for the further development of methods for the directional design of the photoactive fullerene-dye structures -highly effective photosensitizers for photodynamic therapy.