Well I have never been to either Bahia de las Aguilas, Juanillo or Bayahibe...but I can tell you that the pics I've seen from Playa Rincon do not do justice to this beautiful beach. It's probably the best looking / best setup beach I've been to. The only thing is that there's not much out there in terms of food, drinks, etc...which is another reason why I loved it.
The sand over there is absolutely awsome. It has an area which is perfect for bathing because is like a smaller natural lagoon and great for taking a long walk. It's just must not be very photogenic.