  We consider models of accelerating Universe elaborated for Finsler like
gravity theories constructed on tangent bundles to Lorentz manifolds. In the
osculating approximation, certain locally anisotropic configurations are
similar to those for f(R) gravity. This allows us to generalize a proposal (by
Nojiri, Odintsov and Saez-Gomez, arXiv: 1108.0767) in order to reconstruct and
compare two classes of Einstein-Finsler gravity, EFG, and f(R) gravity theories
using modern cosmological data and realistic physical scenarios. We conclude
that EFG provides inflation, acceleration and little rip evolution scenarios
with realistic alternatives to standard Lambda CDM cosmology. The approach is
based on a proof that there is a general decoupling property of gravitational
field equations in EFG and modified theories which allows us to generate
off-diagonal cosmological solutions.
