  Dark energy models with tracker properties have gained attention due to the
large range of initial conditions leading to the current value of the dark
energy density parameter. A well-motivated family of these models are the
so-called $\alpha$-attractors, which show the late time behavior of a
cosmological constant. In the present paper we perform a model-selection
analysis of a variety of $\alpha$-attractor potentials in comparison with a
non-flat $\Lambda$CDM model. Specifically, we compute the Bayes Factor for the
L-Model, the Oscillatory Tracker Model, the Recliner Model, and the Starobinsky
Model, while considering the non-flat $\Lambda$CDM as the base model. Each
model is tested through a Bayesian analysis using observations relevant to the
current accelerated expansion: we employ the latest SNe Ia data, combined with
cosmic clocks, the latest BOSS release of BAO data, and the Planck Compressed
2018 data. The produced Markov Chains for each model are further compared
through a Bayesian evidence analysis. From the latter we conclude that the
Oscillatory Tracker Model is preferred by data (even if weakly) over the
non-flat $\Lambda$CDM model. Our results also suggest at the L-model is the
least favoured version of the $\alpha$-attractor models considered.
