I have had both. Hated the Paraguard and love the Mirena.
Chose the Paraguard because I was still breastfeeding and wanted no hormones. I swear I could feel it in there. Drove me crazy. I don't remember much of the side effects, if any, but I was still nursing so no periods either way. The doctor that removed it about 6 months later told me that there were no nerve endings up there, but perhaps it was just inserted poorly.
Another year later I got the Mirena because my periods were driving me crazy. 7 days long, every 28 days. The Mirena has been perfect. Only side effects are good ones. It took a full year, but I have no period at all. No weight gain or skin issues or anything along those lines.
I vote for Mirena, but it is obviously a very personal choice. Good luck!