We report tests of second- and third-generation density functionals, for pure density functional theory (DFT) and hybrid DFT, against the BH6 representative barrier height database and the AE6 representative atomization energy database, with augmented, polarized double and triple zeta basis sets. The pure DFT methods tested are G96LYP, BB95, PBE, mPWPW91, VSXC, HCTH, OLYP, and OPW91 and the hybrid DFT methods tested are B1B95, PBE0, mPW1PW91, B97-1, B98, MPW1K, B97-2, and O3LYP. The performance of these methods is tested against each other as well as against first-generation methods (BP86, BLYP, PW91, B3PW91, and B3LYP). We conclude that the overall performance of the second-generation DFT methods is considerably better than the first-generation methods. The MPW1K method is very good for barrier height calculations, and none of the pure DFT methods outperforms any of the hybrid DFT methods for kinetics. The B1B95, VSXC, B98, OLYP and O3LYP methods perform best for atomization energies. Using a mean mean unsigned error criterion (MMUE) that involves two sizes of basis sets (both with polarization and diffuse functions) and averages mean unsigned errors in barrier heights and in atomization energy per bond, we find that VSXC has the best performance among pure functionals, and B97-2, MPW1K, and B1B95 have the best performance of all hybrid functionals tested.