I'm on the depo and works for me but I've never had the IUD, my sister in law became pregnant so it put fear into me. The doctors also stated that your womb can reject it and can cause cramps and even come out. I do know a few people who have the IUD and have no issues at all and prefer it to the depo.
However, I can say that the depo makes me almost insane with mood swings for the first few days after having it but then I am fine. I have it every 10 weeks as it stops periods, whereas it isn't always the case at 12 weeks.
It has helped so much with regards to reducing pain, so I can live with the drama for a few days (even if it can be embarrassing when I'm crying at my desk)
This has only been for the last year that this has happened and I have been on it for years.
I would do some research about which is better for you as both have their side effects and can worsen current health issues you may already have.
Hope you find your answers soon

I've tried the Merina IUD to help control bleeding. It was successful in some ways, but I had more cramping I would say and I reacted to the hormone with hives so I had to have it removed. I'm a strange bird though and perhaps it would work well for you.