Generally, from what I understand, the Paraguard means heavier periods with more cramps, and the Mirena means less of a period/no period with fewer cramps because of the way it thins out the endometrium (uterine lining) doe to the localized hormones present in Mirena. It uses a progestin, but a totally different progestin than the one used in Depo-Provera. Mirena uses the progestin found in many combination birth control pills,
levonorgestrel. Technically, because of the hormones, Mirena is considered an intrauterine system.
In my experience with Mirena, I have no period, but no worries about pregnancy either because of the nature of the IUS. There are some features to the Mirena (such as thickened cervical mucus) that outright prevent a sperm getting to an egg. It is one of the most effective methods of birth control, comparable to sterilization.