  We investigate the electronic properties of type-II superconducting Nb(110)
in an external magnetic field. Scanning tunneling spectroscopy reveals a
complex vortex shape which develops from circular via coffee bean-shaped to
elliptical when decreasing the energy from the edge of the superconducting gap
to the Fermi level. This anisotropy is traced back to the local density of
states of Caroli-de-Gennes-Matricon states which exhibits a direction-dependent
splitting. Oxidizing the Nb(110) surface triggers the transition from the clean
to the dirty limit, quenches the vortex bound states, and leads to an isotropic
appearance of the vortices. Density functional theory shows that the Nb(110)
Fermi surface is stadium-shaped near the \Gamma point. Calculations within the
Bogoliubov-de-Gennes theory using these Fermi contours consistently reproduce
the experimental results.
