I can only share my experience from Greenwich Hospital. I chose my Dr (westmed, Rye) partially because they worked out of Greenwich. The peri I had through Westmed did not have privledges there, but he was excellent and thorough. The perinatologists at Greenwich were also very good.
If you have to be admitted for complications, the MFM rooms are very comfortable and the food is amazing. The nursing staff in L&D is incredibly friendly, attentive and thorough. When things went south I was in the OR in 30 min.
And not that you want to think about this, but the NICU is also top notch with an incredible staff.
The only drawback for us was location, we had to travel back and forth almost everyday for the last month I was pregnant and then every day for a 6 week NICU stay. 40 min each way was exhausting after a while.
all worth it though, as my baby is now home and healthy!
HTH