Two series of poly (3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBHV) and poly (3-hydroxybutyrate-co-3-hydroxyhexanoate) (PHBHHx) with different amounts of hydroxyvalerate (HV) and hydroxyhexanoate (HHx) units are compared. The influence of chemical composition on the molecular mobility in quenched samples is discussed, as well as the consequences on the aptitude to crystallize and the microstructures developed during cold-crystallization. In both quenched PHBHV and PHBHHx, Tg decreases as the content of comonomer unit increases. The HHx units (propyl side-groups) are better molecular spacers and produce a stronger Tg shift as compared to the HV units (ethyl side-groups). Copolymerization has no striking effect on the width of the glass transition and the cooperativity length in quenched samples, but in cold-crystallized samples the glass transition is dramatically broadened. When the fully amorphous copolymers are heated from the glassy state to room temperature, crystallization occurs but is largely disrupted, suggesting that the molecular environment in the amorphous phase is significantly changed. The HHx units, which are excluded from the host crystals, delay and slow down the crystallization kinetics in a stronger way as compared to the HV units, which can partially co-crystallize. The obtained crystalline phases are prone to reorganization and the residual amorphous phases appear to have strong differences in composition and large density fluctuations. A practical consequence is that microstructures with different coupling between phases, and thus different properties and stability over time, can be obtained by controlling the nature and content of the comonomer units.