In the archetypal strongly correlated electron superconductor CeCu2Si2 and its Ge-substituted alloys CeCu2(Si1-xGex)2 two quantum phase transitions--one magnetic and one of so far unknown origin-can be crossed as a function of pressure. We examine the associated anomalous normal state by detailed measurements of the low temperature resistivity (rho) power-law exponent alpha. At the lower critical point (at pcl, 1<or=alpha<or=1.5) alpha depends strongly on Ge concentration x and thereby on disorder level, consistent with a Hlubina-Rice-Rosch scenario of critical scattering off antiferromagnetic fluctuations. By contrast, alpha is independent of x at the upper quantum phase transition (at pc2, alpha approximately equal to 1), suggesting critical scattering from local or q=0 modes, in agreement with a density- or valence-fluctuation approach.