Among all the emergent biobased polymers, poly(ethylene 2,5-furandicarboxylate) (2,5-PEF) seems to be particularly interesting for packaging applications. This work is focused on the investigation of the relaxation dynamics and the macromolecular mobility in totally amorphous 2,5-PEF as well as in the less studied poly(ethylene 2,4-furandicarboxylate) (2,4-PEF). Both biopolymers were investigated by differential scanning calorimetry and dielectric relaxation spectroscopy in a large range of temperatures and frequencies. The main parameters describing the relaxation dynamics and the molecular mobility in 2,5-PEF and 2,4-PEF, such as the glass transition temperature, the temperature dependence of the α and β relaxation times, the fragility index, and the apparent activation energy of the secondary relaxation, were determined and discussed. 2,5-PEF showed a higher value of the dielectric strength as compared to 2,4-PEF and other well-known polyesters, such as poly(ethylene terephthalate), which was confirmed by molecular dynamics simulations. According to the Angell’s classification of glass-forming liquids, amorphous PEFs behave as stronger glass-formers in comparison with other polyesters, which may be correlated to the packing efficiency of the macromolecular chains and therefore to the free volume and the barrier properties.