  We present (V,I) photometry of two wide (~25 X 25 arcmin^2) fields centered
on the low surface brightness dwarf spheroidal galaxies Draco and Ursa Minor.
New estimates of the distance to these galaxies are provided
((m-M)_0(UMi)=19.41 \pm 0.12 and (m-M)_0(Dra)=19.84 \pm 0.14) and a comparative
study of their evolved stellar population is presented. We detect for the first
time the RGB-bump in the Luminosity Function of UMi (V_{RGB}^{Bump}=19.40\pm
0.06) while the feature is not detected in Draco. Photometric metallicity
distributions are obtained for the two galaxies and an accurate analysis to
determine the intrinsic metallicity spread is performed by means of artificial
stars experiments. (Abridged) We demonstrate that the inner region of UMi is
significantly structured, at odds with what expected for a system in dynamical
equilibrium. In particular we show that the main density peak of UMi is
off-centered with respect to the center of symmetry of the whole galaxy and it
shows a much lower ellipticity with respect to the rest of the galaxy.
Moreover, UMi stars are shown to be clustered according to two different
characteristic clustering scales, as opposite to Draco, which instead has a
very symmetric and smooth density profile. The possible consequences of this
striking structural difference on our ideas about galaxy formation are briefly
discussed. Combining our distance modulus with the more recent estimates of the
total luminosity of UMi, we find that the mass to light (M/L) ratio of this
galaxy may be as low as M/L ~ 7, a factor 5-10 lower than current estimates.
