We introduce a renormalization-group-invariant (RGI), scheme-independent symmetry ratio ${\kappa }_{AB}$, for the quantitative characterization of symmetry breaking in QCD. As a first application, we employ ${\kappa }_{AB}$ to investigate the relative strength of $SU(2{)}_L\times SU(2{)}_R$ chiral symmetry and $U(1{)}_A$ axial symmetry breaking in $N_f=2+1+1$ lattice QCD using optimal domain-wall fermions at the physical point. Our study covers three lattice spacings and twelve temperatures in the range 164–385~MeV. We examine three independent symmetry-breaking channels in the nonsinglet sector with quark-connected correlators: the $U(1{)}_A$-sensitive scalar–pseudoscalar channel (${\kappa }_{PS}$), probing the $\pi$–$\delta$ system; the $SU(2{)}_L\times SU(2{)}_R$-sensitive vector–axial-vector channel (${\kappa }_{VA}$), probing the $\rho$–$a_1$ system; and an additional $U(1{)}_A$-sensitive tensor vector–axial-tensor vector channel (${\kappa }_{TX}$), probing the ${\rho }_T$–$b_1$ system. At each lattice spacing we observe a clear hierarchy ${\kappa }_{PS}>{\kappa }_{VA}>{\kappa }_{TX}$. Since temperature and lattice spacing are not varied independently in the present ensembles, the lattice-spacing dependence of the hierarchy cannot be isolated, and a controlled continuum extrapolation is deferred to future work.