  We compare the behavior of overlap fermions, which are chirally invariant,
and of Wilson twisted mass fermions at full twist in the approach to the chiral
limit. Our quenched simulations reveal that with both formulations of lattice
fermions pion masses of O(250 MeV) can be reached in practical applications.
Our comparison is done at a fixed value of the lattice spacing a=0.123 fm. A
number of quantities are measured such as hadron masses, pseudoscalar decay
constants and quark masses obtained from Ward identities. We also determine the
axial vector renormalization constants in the case of overlap fermions.
