Composites composed of polyesters, poly(butylene succinate) (PBS) or poly[(butylene succinate)-co-(butylene adipate)] (PBSA), and 5 wt% of montmorillonite (CNa) or organo-modified montmorillonite (C30B) were melt-processed and transformed into films by either compression-molding or extrusion-calendering. XRD, rheological measurements and TEM images clearly indicated that films containing CNa are microcomposites, while nanocomposites were observed for those containing C30B. Using Flash DSC, it was possible, for the first time, not only to measure the heat capacity step at the glass transition of these two materials in their amorphous state, but also to investigate whether the preparation technique influenced the Rigid Amorphous Fraction (RAF) in our PBS- and PBSA-based nanocomposites. In this work, we have successfully shown the correlation between the microstructure of the films and their barrier properties, and especially the role played by the RAF. Indeed, the lowest permeabilities to gases and to water were determined in the films containing the highest RAF in both PBS- and PBSA-based materials.