Despite the knowledge gained in recent years regarding the use of acoustic emissions (AEs) in ecologically friendly, natural fiber-reinforced composites (including certain composites with bio-sourced matrices), there is still a knowledge gap in the understanding of the difference in damage behavior between green and biocomposites. Thus, this article investigates the behavior of two comparable green and biocomposites with tests that better reflect real-life applications, i.e., load-unloading and creep testing, to determine the evolution of the damage process. Comparing the mechanical results with the AE, it can be concluded that the addition of a coupling agent (CA) markedly reduced the ratio of AE damage to mechanical damage. CA had an extremely beneficial effect on green composites because the Kaiser effect was dominant during cyclic testing. During the creep tests, the use of a CA also avoided the transition to new damaging phases in both composites. The long-term applications of PE green material must be chosen carefully because bio and green composites with similar properties exhibited different damage processes in tests such as cycling and creep that could not be previously understood using only monotonic testing.