  We show that the transition between a ETH phase and a many-body localized
phase is marked by the different finite size scaling behaviour of the decay of
the Loschmidt Echo and its temporal fluctuations - after a quantum quench - in
the infinite time limit, despite the fact that the finite time behaviour of
such quantities is dramatically different approach the MBL phase, so that
temporal fluctuations cannot be inferred from the infinite time average of the
Loschmidt Echo. We also show the different scrambling powers of ETH and MBL
Hamiltonians as a probe to the different approaches to equilibrium.
