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The geographical variability, frequency content, and vertical structure of near-surface oceanic kinetic energy (KE) are important for air-sea interaction, marine ecosystems, operational oceanography, pollutant tracking, and interpreting remotely sensed velocity measurements. Here, KE in high-resolution global simulations (HYbrid Coordinate Ocean Model; HYCOM, and Massachusetts Institute of Technology general circulation model; MITgcm), at the sea surface (0 m) and 15 m, are respectively compared with KE from undrogued and drogued surface drifters. Global maps and zonal averages are computed for low-frequency ($<$ 0.5 cpd), near-inertial, diurnal, and semi-diurnal bands. Both models exhibit low-frequency equatorial KE that is low relative to drifter values. HYCOM near-inertial KE is higher than in MITgcm, and closer to drifter values, probably due to more frequently updated atmospheric forcing. HYCOM semi-diurnal KE is lower than in MITgcm, and closer to drifter values, likely due to inclusion of a parameterized topographic internal wave drag. A concurrent tidal harmonic analysis in the diurnal band demonstrates that much of the diurnal flow is non-tidal. We compute a simple proxy of near-surface vertical structure, the ratio of 0 m KE to 0 m KE plus 15 m KE in model outputs, and undrogued KE to undrogued KE plus drogued KE in drifter observations. Over most latitudes and frequency bands, model ratios track the drifter ratios to within error bars. Values of this ratio demonstrate significant vertical structure in all frequency bands except the semidiurnal band. Latitudinal dependence in the ratio is greatest in diurnal and low-frequency bands.