What about synthetic chemical fertilizers used in agriculture? Are they less effective than natural sources, like manure, or compost?

This is true as well, that synthetic fertilizers will lack the seeming and persistent benefit of recycled life forms and other waste products from nature itself. This is yet another of the long, long list of technological solutions that are a mixed blessing and not a total answer without a downside. There will be a degradation of foods made from crops given synthetic nutrients.