We have evaluated the performance of two of the recently developed density functionals (M06-2X and B2PLYP-D), which are widely used, by considering three important prototype systems, including benzeneacetylene, benzenemethane, and benzeneammonia, possessing C-H-...pi or N-H-...pi interactions. Computational results are compared with the available experimental data. Considered density functionals are from two different classes: hybrid meta density functional (M06-2X) and double hybrid density functional (B2PLYP-D). The performance of a range of basis sets (6-31G(d), 6-31+G(d), 6-31+G(d,p), 6-311G(d,p), 6-311+G(d,p), aug-cc-pVXZ (X = D, T, Q)) with the above-mentioned two density functionals was evaluated. Comparison of the results includes Poples basis sets versus Dunnings correlation consistent basis sets with the M06-2X and B2PLYP-D functionals considered in this study. The basis set effect on geometrical parameters, dissociation energies, and selected vibrational frequency shifts was thoroughly analyzed. We have addressed whether the counterpoise corrections with geometry optimizations and vibrational frequencies are important. Our computational study reveals that calculations carried out with smaller basis sets very well reproduce the reported experimental values of dissociation energies. The present study also shows that using the very large Dunnings correlation consistent basis set worsens the results. The necessity of including counterpoise correction for binding energies depends on the system and the type of method used. In general, vibrational frequency calculations using these DFT functionals generate characteristic red shifts for the C-H-...pi or N-H-...pi interactions in the complexes.