They release their nutrients more slowly in the soil, when the plants need them, so they last longer.
The nutrients are contained in complex molecules that won’t leach away with the first rain.
They are less likely to burn the young roots of seedlings. Synthetic fertilizers are made from mineral salts that can kill roots as well as soil microbes if applied improperly.
They enhance soil health by nurturing (or at least not harming) the soil microbes that help make soil nutrients available to plants.