Substitutional cation doping of TiO2 is a topic of great interest, with many studies using first-principles modeling. However, the majority of studies uses standard approximate density functional theory (DFT) exchange-correlation functionals, which suffer from a severely underestimated band gap and the inability to describe localized defect states. DFT corrected for on-site Coulomb interactions (DFT+U) has been a popular choice for rectifying some of the issues with DFT but itself suffers from some important problems, namely, the dependence of material properties on U and the band gap underestimation. It is therefore important to be able to assess the performance of DFT+U against a higher level approach. Hybrid DFT provides such an approach. In this paper, we study Ce and Zr doped into bulk rutile and anatase TiO2, as well as oxygen vacancy formation in doped rutile, using DFT+U and the screened exchange HSE06 implementation of hybrid DFT. Both methods give a qualitatively similar description of a number of properties, such as the stability of the dopant in TiO2 and the effect of doping on the oxygen vacancy formation energies-indicating Ce doping to be effective in reducing the vacancy formation energy, but Zr increases the oxygen vacancy formation energy. However, DFT+U as used in this paper incorrectly predicts a reduced band gap for doped TiO2, which is not seen with HSE06. The band gap underestimation with DFT/DFT+U means that the position of the defect states after oxygen vacancy formation cannot be correctly determined. The effect of these issues with DFT+U on important properties such as reactivity in catalytic reactions needs to be determined, and care must be taken in making any quantitative statements from DFT+U results.