Random structures are typically used for light trapping in thin-film silicon solar cells. However, theoretically periodic structures can outperform random structures in such applications. In this paper we compare random and periodic structures of similar shape. Both types of structure are based on atomic force microscopy (AFM) scans of a sputtered and etched ZnO layer. The absorption in a solar cell on both structures was calculated and compared to external quantum efficiency (EQE) measurements of samples fabricated on the random texture. Measured and simulated currents were found to be comparable. A scalar scattering approach was used to simulate random structures, the rigorous coupled wave analysis (RCWA) to simulate periodic structures. The length and height of random and periodic structures were scaled and changes in the photocurrent were investigated. A high height/length ratio seems beneficial for periodic and random structures. Very high currents were found for random structures with very high roughness. For periodic structures, current maxima were found for specific periods and heights. An optimized periodic structure had a period of Λ = 534 nm and a depth of d = 277 nm. The photocurrent of this structure was increased by 1.6 mA/cm2 or 15% relative compared to the initial (random) structure in the spectral range between 600 nm and 900 nm.