I one was in your same position, trying to figure out whether DEM or CNM was better. What ultimately won me over was the fact that CNMs are legal across the country (DEMs vary by state laws--in some states they can be considered practicing medicine without a license). Also, the route to becoming a DEM was a bit too flexible for me. That is to say, some DEMs are educated at the college level and receive a bachelors or masters in midwifery (but this is the minority of DEMs). The majority receive their education through apprenticeship. This leads to lack of standards. There certainly are DEMs who are well education, well trained, and are fully knowledgeable on what they are doing. But these lax regulations mean that there are a lot of DEMs taking on women that should not be birthing at home. If you are interested in reading more about this, you should check out the blog midwifeology. She was going to be a CPM, and after a lot of soul searching, she decided on CNM.
Finally, I am interested in doing general well-women care, which CNMs practice, whereas DEMs typically only deal with women during pregnancy, labor, delivery, and a short postpartum period. Also, I realized that my philosophy on birth and women's health care would not change no matter the type of midwife I was. Also, the amount of time you spend with a laboring woman depends on the type of practice you work for. Some have midwives stick with their patient throughout their whole pregnancy, labor and delivery. Others have on-call, which as you mentioned, means you would leave at the end of your shift. CNMs do do home births, though. They are in the minority of CNMs, but they are out there.
Just my 2 cents...