We investigate a gas of superfluid fermionic atoms trapped in two hyperfine states by a spherical harmonic potential. We propose a regularization method to remove the ultraviolet divergence in the Hartree-Fock-Bogoliubov equations caused by the use of a zero-range atom-atom interaction. Compared with a method used in the literature, our method is simpler and has improved convergence properties. Then we compare Hartree-Fock-Bogoliubov calculations with the semiclassical local-density approximation. We observe that for systems containing a small number of atoms shell effects, which cannot be reproduced by the semiclassical calculation, are very important. For systems with a large number of atoms at zero temperature, the two calculations are in quite good agreement, which, however, is deteriorated at nonzero temperature, especially near the critical temperature. In this case, the different behavior can be explained within the Ginzburg-Landau theory.