Plasmonic structures interacting with light provide electromagnetic resonances that 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, meanwhile, can serve as an alternative material due to their low-dissipative nature and strong scattering abilities. We studied the optical properties of a system composed of all-dielectric nanoparticle arrays covered with a film of organic dye molecules (IR-792) and compared these dielectric arrays with metallic nanoparticle arrays. We tuned the light-matter interaction by changing the concentration in the dye film and reported the system to be in the strong coupling regime. We observed a Rabi splitting between the surface lattice resonances of the nanoparticle arrays and the absorption line of the dye molecules of up to 253 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 assessed 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 observed no visible Rabi splitting. However, a Rabi splitting evolved at thicknesses from 540 to 990 nm. We performed finite-difference time-domain simulations to analyze the near-field enhancements for the dielectric and metallic nanoparticle arrays. The electric fields were enhanced by a factor of 1200 and 400, close to the particles for gold and amorphous silicon, respectively, and the modes extended over half a micron around the particles for both materials.