Like Babz said, whether you can use a CNM or an OB is not up to your RE at all, but rather your IPs (essentially, is there something in your contract about it or not). If your contract says not allowed, you technically still have the option of discussing it with the IPs if it's really important to you and potentially adding some sort of addendum to the contract (I don't know anything about how that works, but I'm sure you can update it if you're both in agreement). My contract states that I must receive care by a board certified provider, but that encompasses CNMs, so I'm covered.
With my first pregnancy, I was with a practice of several OBs. With my second pregnancy and with this surrogacy, I'm with a practice which includes both CNMs and OBs. Who I see on a given visit depends on both availability and my preferences. Because I have selected that I prefer CNMs, that's who I normally see in my regular visits. If things got complicated (i.e. required surgery), I'd be automatically switched over to an OB. I'll also be able to have a CNM attend the birth, unless it's Sunday since my practice is currently slightly short-staffed.
As for my experiences with each of my previous pregnancies, I do feel like the CNMs give me a little bit more time and personal attention and are just as "go-with-the-flow" as I am about everything (later induction date, etc.). I felt the CNM helped me manage the pain during labor/delivery better than the OB did, but both births felt essentially the same--I had my water broken manually both times and tore both times. I think, regardless of which option you go with, it's more a matter of finding a care provider who is supportive of your wishes. You can find that in both OBs and CNMs.