arimidex acts by blocking the enzyme aromatase subsequently blocking the production of estrogen. nolvadex competitively binds to estrogen receptors in various target tissues. estrogen gets blocked so it can't exert any action.
so the difference is one blocks estrogen and one just prevents it in the first place.
arimidex does a very good job but keep in mind that there are some good things about having a little cholesterol. if you completely block it, then you will lose the good effect on cholesterol that it has. the arimidex will cause a greater suppression of your good (hdl) cholesterol so if you are worried about your cardiovascular health, nolvadex is better.