AgNPs were synthesized by physical, chemical and biological synthesis. The uses of physical and chemical methods in the nanoparticles synthesis are cumbersome and very expensive. The physical and chemical synthesis of
nanoparticles lead to the absorbance of some toxic chemicals on the surface of nanoparticles that may have adverse effects in their applications, so there is an increasing demand to develop low-cost and environmental friendly nanoparticles. For this purpose biological extracts of plants and microbes have been used by researchers to develop low-cost and eco-friendly synthesis of nanoparticles. The
biosynthesis of nanoparticles affectionate several advantages over conventional chemical and physical methods since the methods are easier to carry out and cost-effective.
The one that suits your needs is the best. Green synthesis is just the current trend where you believe that you are protecting the environment by using fermentation broths (for example) that were produced using chemicals with associated carbon-foot prints.
Agreed with the answer of Omar Gonzalez-Ortega. As to why green synthesis is preferred, that would be readily available raw materials like plants and the cost effectivity among major reasons.