Conventional altimetry observations show that mesoscale eddies are ubiquitous and energetic features of the ocean with a universal surface structure. However, these data are subject to objective mapping and limited by coarse resolution. The recently launched Surface Water and Ocean Topography (SWOT) altimeter provides unprecedentedly high-resolution measurements, motivating a comparison of surface eddy structures between SWOT and traditional altimeters. Our study shows that, despite large heterogeneity in individual eddies, global and regional composite eddy structures from both datasets are highly consistent and display a quasi-Gaussian horizontal structure. Further analysis reveals that eddy width, defined as the standard deviation of a Gaussian fit, is significantly larger for small eddies than for large eddies. Reduced-gravity model simulations demonstrate that inverse energy cascade, Rossby wave radiation, and dissipation collectively contribute to this scale-dependent behavior in eddy structure. These findings have important implications for advancing our understanding of the morphology and dynamics of oceanic mesoscale eddies.