  We study deviations between MSSM and NMSSM in the predictions of $\Delta F=2$
processes. We found that there can be two sources which can cause such
deviations, \emph{i.e}, due to certain neutralino-gluino cross box diagrams and
due to well known double penguin diagrams. Both are effective at large $\tan
\beta$. In addition to this, taking into account 8 TeV direct search
constraints from the heavy Higgs searches, we study the maximum allowed MFV
like new physics (NP) effects on $\Delta M_s$ in the two models. In NMSSM such
NP effects can be as large as $25 \%$, on the other hand in MSSM such large
contributions are severely constrained.
