Quasiparticles in the vortex lattice of strongly type-II superconductors are investigated by means of a singular gauge transformation applied to the tight binding lattice Bogoliubov-de Gennes Hamiltonian. Full numerical solutions in the regime of intermediate fields H_{c1} << B << H_{c2} are presented for model superconductors with s-, p- and d-wave symmetries and with square and triangular vortex lattices. For s- and p-wave case we obtain low energy bound states in the core, in agreement with the existing results. For d-wave case only extended quasiparticle states exist. We investigate in detail the nature of these extended states and provide comparison to the previous results within linearized ``Dirac fermion'' model. We stress the importance of internodal interference effects when v ortex and ionic lattices have high degree of commensurability and discuss various specific choices for the singular gauge transformation.