I have employed the disc diffusion method to determine antibacterial properties of iron oxide NPs and their core-shell structures and I have seen many other studies to do the same. Check out these refs:
Better to go with disk diffusion method so you can incubate the plate in inverted position safely. Moreover, well diffusion assay is not standardized as the disk method.
According to studies, the disk diffusion method is a more appropriate method for determining the antibacterial properties of nanoparticles, but the type of microorganism studied in your research is important in choosing a more appropriate method to study the antimicrobial properties of nanoparticles,
Please take a look at the following links for more information:
Article Metal-Based Nanoparticles as Antimicrobial Agents: An Overview
Article Methods for in vitro evaluating antimicrobial activity: A review