  Fanaroff-Riley II low-excitation radio galaxies (FRII-LERGs) are
characterized by weak nuclear excitation on pc-scales and by properties typical
of powerful FRIIs (defined as high-excitation, hereafter HERGs/BLRGs) on
kp-scales. Since a link between the accretion properties and the power of the
produced jets is expected both from theory and observations, their nature is
still debated. In this work we investigate the X-ray properties of a complete
sample of 19 FRII-LERGs belonging to the 3CR catalog, exploiting Chandra and
XMM-Newton archival data. We also analyze 32 FRII-HERGs/BLRGs with Chandra data
as a control sample. We compared FRII-LERG and FRII-HERG/BLRG X-ray properties
and optical data available in literature to obtain a wide outlook of their
behavior. The low accretion rate estimates for FRII-LERGs, from both X-ray and
optical bands, allow us to firmly reject the hypothesis for that they are the
highly obscured counterpart of powerful FRII-HERGs/BLRGs. Therefore, at least
two hypothesis can be invoked to explain the FRII-LERGs nature: (i) they are
evolving from classical FRIIs because of the depletion of accreting cold gas in
the nuclear region, while the extended radio emission is the heritage of a past
efficiently accreting activity; (ii) they are an intrinsically distinct class
of objects with respect to classical FRIs/FRIIs. Surprisingly, in this
direction a correlation between accretion rates and environmental richness is
found in our sample. The richer the environment, the more inefficient is the
accretion. In this framework, the FRII-LERGs are intermediate between FRIs and
FRII-HERGs/BLRGs both in terms of accretion rate and environment.
