  Renormalization group on hierarchical lattices is often considered a valuable
tool to understand the critical behavior of more complicated statistical
mechanical models. In presence of quenched disorder, however, in many model
cases predictions obtained with the Migdal-Kadanoff bond removal approach fail
to quantitatively and qualitatively reproduce critical properties obtained in
the mean-field approximation or by numerical simulations in finite dimensions.
In order to critically review this limitation we analyze the behavior of Ising
and Blume-Emery-Griffiths models on more complicated hierarchical lattices. We
find that, apart from some exceptions, the different behavior appears not only
limited to Midgal-Kadanoff-like cells but is associated right to the
hierarchization of Bravais lattices in small cells also when in-cell loops are
considered.
