Hopefully you've made your decision by now, but from my own research, I would say there is no obvious difference between them. It very much just depends on your body and what your cycles were like before. Obviously, the sooner it happens, the sooner you can get back to ttc, so in that sense a d&c or a medical miscarriage is likely to be faster than waiting for it to happen naturally. But you also don't know how you'll feel and you may want a bit of a break after anyway.
To give you a sense of my own experience, I had a missed miscarriage that I found out about at 8 weeks. Baby stopped developing at 5 weeks. I preferred to wait it out and we waited until 11 weeks with no sign of anything happening soon. So because I really needed to get back to work (I travel part of the week for work, so I couldn't because I didn't want to be risk stuck away from home on my own and miscarrying, so I had to take off time), we decided to opt for the d&c. There is a very, very tiny risk of fertility issues after a d&c (about 1 in 300 might develop problems they didn't have before, of course, there is always a risk of secondary infertility after any pregnancy so you could experience problems even after a natural miscarriage too). But my midwife strongly recommended the d&c over the medical management, particularly because both a natural and medically managed miscarriage still leave open the risk of needing a d&c anyway if there are complications (this happened to a friend of mine a few weeks previously).
It all went smoothly and actually I think it was a much more positive experience than if I can chosen either other option, just because I had already been waiting so long and I was ready to move on. Many ladies seem to get their periods again about 4-6 weeks later, though it can take longer of course, especially if you have irregular cycles anyway. I have regular cycles and have gotten pregnant easily both times, and I'm almost certain I ovulated 2 weeks after the d&C. I don't really know and we aren't ttc because I want to have one natural period first and then we'll try that cycle. But I got all my usual ovulation signs (it's really obvious to me when I'm ovulating, I don't really even need to track it) and I also got two days of + on an opk those days, which went back to negative after. So who knows? But I suspect I'll get my period later this week and we'll be trying again this month.
Sorry for your loss and hope you've decided what you want to do next and are ready to start moving forward whatever you choose. I felt much better myself once I made the decision and knew what would happen.
