Organic apricots are juicier and generally even taste better than non-organic apricots. All apricots need to be harvested carefully due to their thin skins and delicate nature, but organic apricots need an even lighter touch to avoid bruising.
In addition to tasting better than normally grown apricots, organic-grown apricots are better for the environment due to the absence of chemical pesticide sprays. Not using chemicals is easier on the wallet; apricots can be grown more cheaply by growing directly from seed instead of purchasing a cutting from a parent tree.
Growing organically means forsaking chemicals harmful to the environment and other plants, like herbicides to kill weeds and pesticides to repel insects that afflict apricots like tent caterpillars. Without these chemicals, organic apricots tend to be "uglier" than their non-organic counterparts in the supermarket.