At my MW's advising, I recently made an appointment with OBs/midwives at my local--and very well-known--medical center. I started the pregnancy with OB care in another state, and was able to decide what I wanted done. Now, all I need is a GBS test (in case of transfer), and some blood tests to check my iron levels. I preferred to go through the hospital, as insurance covers it, whereas it would be an additional expense through my MW. And if I needed to transfer, I wanted to see where I would be going.
Since I was seeking care at a late-ish date, the OB called me directly. Within the span of a 5-minute conversation, I received a flustered lecture on how my MW should be doing the tests, that I couldn't just "use" the hospital for diagnostics then deliver with a MW, and told I would probably need a c-section since my baby is breech...at 34 weeks. It was fine over the phone, because I could hide the nonverbal reactions to this ridiculousness, but that won't be so easy in person.
It's just a matter of how comfortable you feel navigating the system, and determining whether the frustrations outweigh the benefits.