  In this article we analyze the impact of B-physics and Higgs physics at LEP
on standard and non-standard Higgs bosons searches at the Tevatron and the LHC,
within the framework of minimal flavor violating supersymmetric models. The
B-physics constraints we consider come from the experimental measurements of
the rare B-decays b -> s gamma and B_u -> tau nu and the experimental limit on
the B_s -> mu+ mu- branching ratio. We show that these constraints are severe
for large values of the trilinear soft breaking parameter A_t, rendering the
non-standard Higgs searches at hadron colliders less promising. On the contrary
these bounds are relaxed for small values of A_t and large values of the
Higgsino mass parameter mu, enhancing the prospects for the direct detection of
non-standard Higgs bosons at both colliders. We also consider the available
ATLAS and CMS projected sensitivities in the standard model Higgs search
channels, and we discuss the LHC's ability in probing the whole MSSM parameter
space. In addition we also consider the expected Tevatron collider
sensitivities in the standard model Higgs h -> b bbar channel to show that it
may be able to find 3 sigma evidence in the B-physics allowed regions for small
or moderate values of the stop mixing parameter.
