Semiconducting single-walled carbon nanotubes' (SWCNTs) broad absorption range and all-carbon composition make them attractive materials for light harvesting. We report photoinduced charge transfer from both multichiral and single-chirality SWCNT films into atomically flat SnO2 and TiO2 crystals. Higher-energy second excitonic SWCNT transitions produce more photocurrent, demonstrating carrier injection rates are competitive with fast hot-exciton relaxation processes. A logarithmic relationship exists between photoinduced electron-transfer driving force and photocarrier collection efficiency, becoming more efficient with smaller diameter SWCNTs. Photocurrents are generated from both conventional sensitization and in the opposite direction with the semiconductor under accumulation and acting as an ohmic contact with only the p-type nanotubes. Finally, we demonstrate that SWCNT surfactant choice and concentration play a large role in photon conversion efficiency and present methods of maximizing photocurrent yields.