The current research is devoted to the development and characterization of green antimicrobial polymer biocomposites for food packaging applications. The biocomposites were developed by melt compounding on the basis of two different succinate polymer matrices with varying chain stiffness—polybutylene succinate (PBS) or its copolymer with 20 mol.% of polybutylene adipate (PBSA). Fungi chitosan oligosaccharide (C98) and crustacean chitosan (C95) were used as antimicrobial additives. The rheological properties of the developed biocomposites were determined to clear out the most suitable temperature for melt processing. In addition, mechanical, thermal, barrier and antimicrobial properties of the developed biocomposites were determined. The results of the investigation revealed that PBSA composites with 7 wt% and 10 wt% of the C98 additive were more suitable for the development of green packaging films because of their higher ultimate elongation values, better damping properties as well as their superior anti-microbial behavior. However, due to the lower thermal stability of the C98 additive as well as PBSA, the melt processing temperatures of the composites desirably should not exceed 120 °C. Additionally, by considering decreased moisture vapor barrier properties, it is recommended to perform further modifications of the PBSA-C98 composites through an addition of a nanoclay additive due to its excellent barrier properties and thermal stability.