We present a comparative assessment of the accuracy of two different approaches for evaluating dispersion interactions: inter-atomic pair-wise corrections and semi-empirical meta-generalized-gradient-approximation (meta-GGA) based functionals. This is achieved by employing conventional (semi-)local and (screened-)hybrid functionals, as well as semi-empirical hybrid and non-hybrid meta-GGA functionals of the M06 family, with and without inter-atomic pair-wise Tkatchenko-Scheffler corrections. All those are tested against the benchmark S22 set of weakly bound systems, a representative larger molecular complex (dimer of NiPc molecules), and a representative dispersively bound solid (hexagonal boron nitride). For the S22 database, we also compare our results with those obtained from the pair-wise correction of Grimme (DFT-D3) and non-local Langreth-Lundqvist functionals (vdW-DF1 and vdW-DF2). We find that the semi-empirical kinetic-energy-density dependence introduced in the M06 functionals mimics the non-local correlation needed to describe dispersion. However, long-range contributions are still missing. Pair-wise inter-atomic corrections, applied to conventional semi-local or hybrid functionals, or to M06 functionals, provide for a satisfactory level of accuracy irrespectively of the underlying functional. Specifically, screened-hybrid functionals such as the Heyd-Scuseria-Ernzerhof (HSE) approach reduce self-interaction errors in systems possessing both localized and delocalized orbitals, and can be applied to both finite and extended systems. Therefore, they serve as a useful underlying functional for dispersion corrections.