We present results for the $SU(3)$ breaking ratios of decay constants $f_{D_s}/f_D$ and $f_{B_s}/f_B$ and - for the first time with physical pion masses - the ratio of bag parameters $B_{B_s}/B_{B_d}$, as well as the ratio $xi$, forming the ratio of the nonpeturbative contributions to neutral $B_{(s)}$ meson mixing. Our results are based on Lattice QCD simulations with chirally symmetric 2+1 dynamical flavors of domain wall fermions. Eight ensembles at three different lattice spacing in the range $a = 0.11 - 0.07,mathrm{fm}$ enter the analysis two of which feature physical light quark masses. Multiple heavy quark masses are simulated ranging from below the charm quark mass to half the bottom quark mass. The $SU(3)$ breaking ratios display a very benign heavy mass behaviour allowing for extrapolation to the physical bottom quark mass. The results in the continuum limit including all sources of systematic errors are $f_{D_s}/f_D = 1.1740(51)_mathrm{stat}(^{+68}_{-68})_mathrm{sys}$, $f_{B_s}/f_B = 1.1949(60)_mathrm{stat}(^{+hphantom{0}95}_{-175})_mathrm{sys}$, $B_{B_s}/B_{B_d} = 0.9984(45)_mathrm{stat}(^{+80}_{-63})_mathrm{sys}$ and $xi = 1.1939(67)_mathrm{stat}(^{+hphantom{0}95}_{-177})_mathrm{sys}$. Combining these with experimentally measured values we extract the ratios of CKM matrix elements $|V_{cd}/V_{cs}| = 0.2164(57)_mathrm{exp}(^{+12}_{-12})_mathrm{lat}$ and $|V_{td}/V_{ts}| = 0.20329(41)_mathrm{exp}(^{+162}_{-301})_mathrm{lat}$.
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