We study deviations between MSSM and $Z_3$-invariant NMSSM, with respect to their predictions in $Delta F=2 $ processes. We find that potentially significant effects arise either from the well known double-penguin diagrams, due to the extra scalar NMSSM states, or from neutralino-gluino box contributions, due to the extended neutralino sector. Both are discussed to be effective in the large $tanbeta$ regime. Enhanced genuine-NMSSM contributions in double penguins are expected for a light singlet spectrum (CP-even,CP-odd), while the magnitude of box effects is primarily controlled through singlino mixing. The latter is found to be typically subleading (but non-negligible) for $lambda lesssim 0.5$, however it can become dominant for $lambdasim mathcal{O}(1)$. We also study the low $tanbeta$ regime, where a distinction between MSSM and NMSSM can come instead due to experimental constraints, acting differently on the allowed parameter space of each model. To this end, we incorporate the LHC Run-I limits from $Hrightarrow Z Z$, $A rightarrow hZ$ and $H^pm rightarrow tau u $ non-observation along with Higgs observables and set (different) upper bounds for new physics contributions in $Delta F=2 $ processes. We find that a $sim 25%$ contribution in $Delta M_{s(d)}$ is still possible for MFV models, however such a large effect is nowadays severely constrained for the case of MSSM, due to stronger bounds on the charged Higgs masses.
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