I've had both at various times, and currently have the Mirena which is the hormonal one. I am not aware that there's any link with cancer but that's something to check with your doctor.
I really love the Mirena. I had a huge problem with the non hormone IUD as I had incredibly heavy bleeding which I ended up needing medication to control. After my second baby I found my periods getting worse and worse (V bad bleeding) so I got the Mirena both to control that and for birth control. It really is great. I still get periods but they are way lighter and now much more manageable - I know a lot of people stop getting periods at all with Mirena. The bleeding was irregular at first but this was OK as it was light, and it settled down after a few months - I have had it 3 years now and get regular light periods.
The hormone dose is very low, so even if you've had problems with hormones eg the Pill in the past, the Mirena can be fine - the pill didn't suit me but Mirena is fine. The hormone has actually helped me eg I hardly get PMS at all now which is a bonus!!
It is wonderful not to have to think about birth control - it's a few minute procedure to get it in, and then you can forget about it for 5 years. It's a little uncomfortable to have it in, but it's very quick, and I had cramping for about 24 hours, then nothing more.
It's certainly one of the lowest doses of hormones you can have, much lower than the pill. I'd give it a try and see how you like it. You can always have it out if it doesn't work for you