Nanohole arrays in metal films allow extraordinary optical transmission (EOT); the phenomenon is highly advantageous for biosensing applications. In this article, we theoretically investigate the performance of refractive index sensors, utilizing square and hexagonal arrays of nanoholes, that can monitor the spectral position of EOT signals. We present near- and far-field characteristics of the aperture arrays and investigate the influence of geometrical device parameters in detail. We numerically compare the refractive index sensitivities of the two lattice geometries and show that the hexagonal array supports larger figure-of-merit values due to its sharper EOT response. Furthermore, the presence of a thin dielectric film that covers the gold surface and mimics a biomolecular layer causes larger spectral shifts within the EOT resonance for the hexagonal array. We also investigate the dependence of the transmission responses on hole radius and demonstrate that hexagonal lattice is highly promising for applications demanding strong light transmission. ; Brno University of Technology (Project CZ.1.07/2.3.00/30.0039)