Becke'13 (B13) is a general density functional theory (DFT) designed for strongly correlated molecules. Kong-Proynov'16/B13 (KP16/B13) is a modification of B13 that treats the correlation kinetic term through modeling the adiabatic connection and contains fewer parameters. A question remains whether functionals designed for extremely strong correlations can handle correlation of normal strength. In this work, both functionals are benchmarked with a variety of molecular systems from the Minnesota-2015 datasets and compared with the mainstream functionals such as B3LYP and a spectrum of other types of functionals, as well as Becke'05 (B05), the predecessor of B13. Our calculations, made possible with an efficient self-consistent-field implementation of those new functionals, show that B05, B13, and KP16/B13, based on full HF exchange, recover a majority of the correlation where it is very significant (i.e., where HF has large errors). They perform very well for reaction barriers. On the other hand, their performance on multireference systems is mixed. Overall, B05, B13, and KP16/B13 are competitive to B3LYP, and B05 is even competitive to heavily parameterized functionals for most sets despite containing 100% HF exchange. KP16/B13, in particular, contains only three empirical parameters, demonstrating the possibility of treating correlation of all strength with single-determinant Kohn-Sham DFT.