Solar prominences are formed by partially ionized plasma with inter-particle collision frequencies generally warranting magnetohydrodynamic treatment. In this work we explore the dynamical impacts and observable signatures of two-fluid effects in the parameter regimes when ion-neutral collisions do not fully couple the neutral and charged fluids. We perform 2.5D two-fluid (charges-neutrals) simulations of the Rayleigh-Taylor instability (RTI) at a smoothly changing interface between a solar prominence thread and the corona. The purpose of this study is to deepen our understanding of the RTI and the effects of the partial ionization on the development of RTI using nonlinear two-fluid numerical simulations. Our two-fluid model takes into account neutral viscosity, thermal conductivity, and collisional interaction between neutrals and charges: ionization-recombination, energy and momentum transfer, and frictional heating. In this paper, the sensitivity of the RTI dynamics to collisional effects for different magnetic field configurations supporting the prominence thread is explored. This is done by artificially varying, or eliminating, effects of both elastic and inelastic collisions by modifying the model equations. We find that ionization and recombination reactions between ionized and neutral fluids do not substantially impact the development of the primary RTI. However, such reactions can impact the development of secondary structures during the mixing of the cold prominence and hotter surrounding coronal material. We find that collisionality within and between ionized and neutral particle populations plays an important role in both linear and nonlinear development of RTI; ion-neutral collision frequency is the primary determining factor in development or damping of small-scale structures. We also observe that the degree and signatures of flow decoupling between ion and neutral fluids can depend on the inter-particle collisionality and on the magnetic field configuration of the prominence thread.