Plasmon resonances in metallic nanoparticles augment the Förster resonance energy transfer (FRET) between two molecules. We calculate and analyze comparatively the enhancement factors of FRET for a metallic nanosphere and for a metallic spherical nanoshell by finite element method (FEM). These calculations are compared with analytical results obtained from the knowledge of spectral properties of the Neumann-Poincaré (electrostatic) operator for sphere. With respect to the plain metallic nanosphere, the spherical nanoshell shows a greater tunability of energy range for which the energy transfer is enhanced. Our work can be relevant for using FRET for various applications regarding porous materials.