Thin films containing metal nanohole arrays can be fabricated with high precision, and regular, tunable features via colloidal lithography. They are ideal model structures to study the relation between structural design and optoelectronic properties, for example as transparent, conducting electrodes, where the percolation threshold sets an upper limit on the achievable transparency. An important, but less systematically studied property of transparent conductive electrodes is the amount of scattered light, as described by the haze factor. Here, the influence of structural parameters on the resulting haze factor of metal nanohole array films is investigated. It is found that transmission, transparency, and haze factor cannot be independently controlled, and propose a new fabrication paradigm to optimize the optoelectronic properties of such films. Hierarchical metal micro/nanohole array films are designed, which combine precisely controlled and highly regular structural features at two length scales. These hierarchical structures maximize transparency while simultaneously providing low haze factors. Computer simulations based on finite elements and ray optics are in close agreement with the experimental results and reveal that the reduced haze factor results from a drastic decrease of grating diffraction efficiency in the hierarchical films.