The simplist answer is that the green method creates a molecule that is slightly different than the chemical pathway, thus altered antimicrobial activity.
Can you elaborate? "Green" has no technical meaning - what were the synthetic protocols? What was the protocol by which efficacies were compared, relevant data and their statistical treatment?
Apparently, looking at the previous reports of green synthesis of any molecule, the properties revealed out from green synthesis are slightly different from chemical synthesis. Many times green synthesis is superior or sometimes its shows declining results.