Natasha has as usual provided useful and accurate information. However, she may have left out the most important thing in why to prefer Samana to Punta Cana: The nature itself.
Ever been to the extreme West of Bretagne/Britanny in France? Samana is like a tropical version of that.
Samana is wild, verdant, with coves, bays, rocks, low mountains, awe inspiring views. Also, as Natasha explained, it is not as dominated by tourism, and a large amount of the hotels there are small and family owned, providing a different atmosphere to the huge all inclusives. The town of Samana itself is interesting, especially the market.
I have been to Playa El Valle and it is spectacular, surrounded by wild mountains and vegetation green and lush enough to be called rain forest. The sands are dark, almost coal coloured, which is rare in Samana where the beaches are normally creamy golden. Don't count on being able to swim from El Valle, though. When the waves come thundering in straight from the Atlantic, the undertow and the waves themselves are far too dangerous. More than one tourist has tried to do so and died in the attempt. In calm waters I suppose it is safe enough, and at low tide I have heard there should be a small stream making a pool right before the ocean.
Rincon is everything Natasha said. You can go there by boat, 4WD or horse. The boat ride is great.
Regards,
Susanne