The design of highly efficient sensitizers is one of the most significant areas in dye-sensitized solar cell (DSSC) research. We studied a series of benzothiadiazole-based D-π-π-A organic dyes, putting emphasis on the influence of the donor moiety on the DSSC’s efficiency. Using (linear-response time-dependent) density functional theory ((TD)DFT)) with the CAM-B3LYP functional, different donor groups were characterized in terms of electronic absorption spectra and key photovoltaic parameters. As a reference, a dye was considered that had a benzothiadiazole fragment linked via thiophene rings to a diphenylamine donor and a cyanoacrylic-acid acceptor. The different systems were first studied in terms of individual performance parameters, which eventually aggregated into power conversion efficiency. Only the amino-substituted species showed a modest increase, whereas the dimethylamino case showed a decrease.