  We investigate a generalized form of the phenomenologically emergent dark
energy model, known as generalized emergent dark energy (GEDE), introduced by
Li and Shafieloo [Astrophys. J. {\bf 902}, 58 (2020)] 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
phenomenologically emergent dark energy (PEDE) (corresponds to $\Delta=1$)
models, allowing us to determine which model is preferred most by the fit of
the observational datasets. We find evidence in favor of the GEDE model for
Planck alone and in combination with R19, while the Bayesian model comparison
is inconclusive when Supernovae Type Ia or BAO data are included. 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 $1\sigma$ CL.
