Yes, both silver and copper are antimicrobial. As far as I know, silver has zero nutritional value. Copper is a micronutrient useful to humans.
If you want antimicrobial metal kitchenware, copper makes more sense than silver, though it should still not be overused.
Additionally, copper surfaces in hospitals have a proven track record of helping to kill infection and reduce the transmission of hospital acquired infections.
If you can afford it (as it isn't cheap) and want to Prep for a post antibiotic world, copper fixtures of various sorts in your home would not be a bad idea.
https://en.wikipedia.org/wiki/Oligodynamic_effect