Hi there. Well I've only been to the Playa Dorada and I had a wonderful holiday there - although it was more than 10 years ago (it was by far the cheapest caribbean type holiday at that time).
The differences with the beaches are the ones on the atlantic coasts are not so picture postcard perfect (as in pinky coloured sands etc.) and the water is colder and choppier. It's still very beautiful in my opinion.
I think if you are after that caribbean experience with the nicest of beaches with the softest sands and the calm waters the caribbean coasts will suit you best - I have heard very good reports about the Bavaro resort area.
Sorry I can't help more, as I have only been on the atlantic side, but I can say I had a wonderful time and the beaches at Playa Dorada are really lovely in their own right.
*It is not necessary to understand things in order to argue about them. -- Pierre De Beaumarchais
We have booked the Dominican Republic for our honeymoon in August, we didnt know where to go, we have decided to go to Sosua, so you're just as in the dark as we are, but I still think it'll be a lovely holiday wherever you go in DR, so many people I have spoken to have said they have been there and they would recommend it to anyone...good luck