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To assess the title issue, 38 hydrogen transfer barrier heights and 38 non-hydrogen transfer barrier heights/isomerizations extracted from extensive databases have been considered, in addition to 4 2 p-isomerization reactions and 6 others for large organic molecules. All Kohn-Sham DFT calculations have employed the popular M06-2X functional, whereas the correlated molecular orbital (MO)-based ones are from single-reference MP2 and CCSD(T) methods. They have all utilized the same basis sets, with raw MO energies subsequently extrapolated to the complete basis set limit without additional cost. MP2 calculations are found to be as cost-effective as DFT ones and often slightly more, while showing a satisfactory accuracy when compared with the reference data. Although the focus is on barrier heights, the results may bear broader implications, in that one may see successes and difficulties of DFT when compared with traditional MO theories for the same data. [ABSTRACT FROM AUTHOR]