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The Strongly Constrained and Appropriately Normed (SCAN) functional is a non-empirical meta-generalized-gradient approximation (meta-GGA) functional that satisfies all the known constraints that a meta-GGA functional can, but it also exhibits a great degree of sensitivity to numerical grids. Its numerical complexities are amplified when used in Perdew-Zunger (PZ) self-interaction correction (SIC) which requires evaluating energies and potentials using orbital densities that vary far more rapidly than spin densities. Recent regularization of the SCAN functional (rSCAN) simplifies numerical complexities of SCAN at the expense of violation of some exact constraints. To develop a good understanding of the performance of rSCAN and the effect of loss of an exact constraint at the limit of slowly varying density, we have compared its performance against SCAN for vibrational frequencies, infra-red and Raman intensities of water clusters, electric dipole moments, spin magnetic moments of a few molecular magnets, weak interaction energies of dimers, barrier heights of reactions, and atomization energies for benchmark sets of molecules. Likewise, we examined the performance of SIC-rSCAN using the PZ-SIC method by studying atomic total energies, ionization potentials and electron affinities, molecular atomization energies, barrier heights, and dissociation and reaction energies. We find that rSCAN requires a much less dense numerical grid and gives very similar results as SCAN for all properties examined with the exception of atomization energies which are somewhat worse in rSCAN. On the other hand, SIC-rSCAN gives marginally better performance than SIC-SCAN for almost all properties studied in this work.