  One of the possible ways to explain the observed flavour structure of
fundamental particles is to include flavor symmetries in the theories. In this
work, we investigate the rare charged lepton flavour violating (cLFV) decay
process ($\mu \rightarrow e\gamma$) in two of the low scale ($\sim$TeV) seesaw
models: (i) the Inverse seesaw (ISS) and (ii) Linear seesaw (LSS) models within
the framework of $A_{4}$ flavour symmetry. Apart from the $ A_{4} $ flavour
symmetry, some other symmetries like $U(1)_{X}$, $Z_4$ and $Z_5$ are included
to construct the Lagrangian. We use results from our previous work
\cite{Devi:2021ujp,Devi:2021aaz} where we computed unknown neutrino oscillation
parameters within $3 \sigma$ limits of their global best fit values, and apply
those results to compute the branching ratio (BR) of the muon decay for both
the seesaw models. Next we compare our results with the current experimental
bounds and sensitivity limits of BR($\mu \rightarrow e\gamma$) as projected by
various experiments, and present a comparative analysis that which of the two
models is more likely to be tested by which current/future experiment. This is
done for various values of currently allowed non-unitarity parameter. This
comparative study will help us to pinpoint that which of the low scale seesaw
models and triplet flavon VEV alignments will be more viable and favourable for
testing under a common flavour symmetry ($A_{4}$ here), and hence can help
discriminate between the two models.
