I've had Mirena and Paragard so I'll give you my experience with both.
With Mirena, I experienced a month of bleeding after insertion (um... suck!) but afterwards it tapered off and I didn't get another (mostly due to PCOS) but it does cause lighter more infrequent periods. What I disliked was the hormones, which, although light, still affected me. I'm very sensitive to them and have to be very selective which I use and can tolerate. Insertion hurt much like a menstral cramp but nothing intolerable.
I prefer Paragard because it lasts 10 years and is hormone free. I didn't experience the same post-insertion bleeding however, I had it placed at my 6 week post partum check up so that means squat. It works in a similar fashion to Mirena but has copper instead of hormones. I'm no expert how exactly
how this all works but there's tons of info out there. Most can use Paragard unless you have an uncommon allergy to copper. The lack of hormones in this particular IUD allows me to take birth control pills with the exact type and amount of hormones I can tolerate to regulate my period as needed for my PCOS.
I use both because I'm not always the best when it comes to remembering a pill, have issue with other forms of BC (shot, patches, rings, etc.) and sure as heck don't want a 3rd child in our current situation!
I've been able to lose weight on both Mirena and Paragard. Mirena I lost around 20 pounds in 2 months before getting pregnant again and then my current weight loss is with Paragard.
So just remember, if you think an IUD is the way you'd like to go, you might want to consider both forms and discuss your options with your doctor. Good luck!