Plasmonic structures interacting with light provide electromagnetic resonances which result in a high degree of local field confinement enabling the enhancement of light-matter interaction. Plasmonic structures typically consist of metals which, however, suffer from very high ohmic losses and heating. High-index dielectrics, on the other hand, can serve as an alternative material due to their low-dissipative nature and strong scattering abilities. We study the optical properties of a system composed of all-dielectric nanoparticle arrays covered with a film of organic dye molecules (IR-792), and compare these dielectric arrays with metallic nanoparticle arrays. We tune the light-matter interaction by changing the concentration in the dye film and report the system to be in the strong coupling regime. We observe a Rabi splitting between the surface lattice resonances (SLRs) of the nanoparticle arrays and the absorption line of the dye molecules of up to 253 meV and 293 meV, for the dielectric and metallic nanoparticles, respectively. The Rabi splitting depends linearly on the square root of the dye molecule concentration , and we further assess how the Rabi splitting depends on the film thickness for a low dye molecule concentration. For thinner films of thicknesses up to 260 nm, we observe no visible Rabi splitting. However, a Rabi splitting evolves at thicknesses from 540 nm to 990 nm. We perform finite-difference time-domain simulations to analyze the near-field enhancements for the dielectric and metallic nanoparticle arrays. The electric fields are enhanced by a factor of 1200 and 400, close to the particles for gold and amorphous silicon, respectively, and the modes extend over half a micron around the particles for both materials.