Mirena is a newer type of IUD, it is plastic and uses the same contraceptive method as the pill.
I got it because I had heaps of side effects with the pill and also kept forgetting to take it!
This is the
Mirena site it does comparisions with other IUD's in the FAQ section.
(Of course it is a completely biased POV though!)
The main drawback I found was the cost. if you're not able to have it subsidised it is around $350, compared to $30 for the copper IUD.
I justified the expense by working out what I would be saving on tampons and pads and painkillers in the 5 years worth of periods I wouldn't be getting and that won hubby over!