Specific heat $C(T)$ and electrical resistivity $\ensuremath{\rho}(T)$ of ${\mathrm{CeCu}}_{6\mathrm{\ensuremath{-}}x}{\mathrm{Au}}_{x}$ at very low temperatures T show distinctly different behavior depending on whether long-range antiferromagnetic order is suppressed by hydrostatic pressure p or an applied magnetic field B. p tuning yields $C/T=a\mathrm{ln}{(T}_{0}/T)$ and $\ensuremath{\rho}\ensuremath{\approx}{\ensuremath{\rho}}_{0}{+A}^{\ensuremath{'}}T,$ while B tuning shows $C/T={\ensuremath{\gamma}}_{0}\ensuremath{-}{a}^{\ensuremath{'}}{T}^{0.5}$ and $\ensuremath{\rho}\ensuremath{\approx}{\ensuremath{\rho}}_{0}{+A}^{\ensuremath{''}}{T}^{1.5}.$ This suggests that the spectrum of low-lying excitations that determines the behavior near these quantum phase transitions differs.