  We investigate a generalized form of the Phenomenologically Emergent Dark
Energy (PEDE) model, known as Generalized Emergent Dark Energy (GEDE),
introduced in~\cite{Li:2020ybr} in light of a series of cosmological probes and
considering the evolution of the model at the level of linear perturbations.
This model introduces a free parameter $\Delta$ that can discriminate between
the $\Lambda$CDM (corresponds to $\Delta=0$) or the PEDE (corresponds to
$\Delta=1$) models, allowing us to determine which model is preferred most by
the fit of the observational datasets. We find a strong evidence of the GEDE
scenario for most of the employed observational datasets. In particular, we
find that $\Lambda$CDM model is disfavored at more than $2\sigma$ CL for most
of the observational datasets considered in this work and PEDE is in agreement
with Planck 2018+BAO+R19 combination within $1\sigma$. Finally, a Bayesian
Model comparison shows a strong evidence for GEDE against $\Lambda$CDM for most
of the dataset combinations.
