  Unimodular Gravity is normally assumed to be equivalent to General Relativity
for all matters but the character of the Cosmological Constant. Here we discuss
this equivalence in the presence of a non-minimally coupled scalar field. We
show that when we consider gravitation to be dynamical in a QFT sense, quantum
corrections can distinguish both theories if the non-minimal coupling is
non-vanishing. In order to show this, we construct a path integral formulation
of Unimodular Gravity, fixing the complicated gauge invariance of the theory
and computing all one-loop divergences. We find a combination of the couplings
in the Lagrangian to which we can assign a physical meaning. It tells whether
quantum gravitational phenomena can be ignored or not at a given energy scale.
Its renormalization group flow differs depending on if it is computed in
General Relativity or Unimodular Gravity.
