Two particle image velocimetry arrangements are used to make true spatial comparisons between smooth- and rough-wall boundary layers at high Reynolds numbers across a very wide range of streamwise scales. Together, the arrangements resolve scales ranging from motions on the order of the Kolmogorov microscale to those longer than twice the boundary layer thickness. The rough-wall experiments were obtained above a continuous sandpaper sheet, identical to that used by Squire et al. [J. Fluid Mech. 795, 210 (2016)], and cover a range of friction and equivalent sand-grain roughness Reynolds numbers ($12000\lesssim {\delta }^{+}\lesssim$ 18000, $62\lesssim k_s^{+}\lesssim 104$). The smooth-wall experiments comprise new and previously published data spanning $6500\lesssim {\delta }^{+}\lesssim 17000$. Flow statistics from all experiments show similar Reynolds number trends and behaviors to recent, well-resolved hot-wire anemometry measurements above the same rough surface. Comparisons, at matched ${\delta }^{+}$, between smooth- and rough-wall two-point correlation maps and two-point magnitude-squared coherence maps demonstrate that spatially the outer region of the boundary layer is the same between the two flows. This is apparently true even at wall-normal locations where the total (inner-normalized) energy differs between the smooth and rough wall. Generally, the present results provide strong support for Townsend's [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1956), Vol. 1] wall-similarity hypothesis in high Reynolds number fully rough boundary layer flows.

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• Structure & turbulence of boundary layers