Maybe you can try the same question at /r/AskSocialScience, as it seems to fit there too.

Anyway, I figured James Robinson and Daron Acemoglu might have an opionion on this, and it turns out they do! Here's a small excerpt:

One hypothesis about the divergence between Haiti and the Dominican Republic is that a similar situation arose with Haiti and the Dominican Republic. Though the latter shared a history of slavery, dictatorship and US invasion, it did not suffer as much as Haiti. After 1930 Rafael Trujillo, head of the US created national guard, set himself up as dictator. He controlled the army and embarked on a path of extractive economic growth. As the world economy boomed after 1945, divergence set in. The Dominican Republic exported sugarcane and cigars; afterwards they developed a successful export processing zone. After Trujillo was assassinated in 1961, they managed an imperfect transition to more inclusive political institutions, sustaining the economic growth. Haiti was different, without such a strong state or political control of the army, the period after 1930 saw political instability not extractive growth and when François Duvalier (“Papa Doc”) came to power in 1957 he privatized violence using the ton ton macoutes to control the country, not the army. There was no extractive growth in Haiti, just anarchy.

All the same, this is just one hypothesis that fits the facts, the divergence between the two halves of the island of Hispaniola remains a major puzzle.

It should be noted that this is from the blog about their book "Why Nations Fail", which argues the main driver of economic progress has been what they term "inclusive institutions". I'm not doing the book any justice by this short description, but this does explain why they focus on this aspect in their explanation.

I'm Dominican and love history and have made a point to study the history of both countries as much as I could. Before I answer let me say that you can't really say that the D.R. and Haiti were "once the same nation" as it implies that they were together for a really long time and separated...and that's not the case.

Once the Spanish and the French formally divided the island among themselves the path taken by both territories was so different that you couldn't really say they were the same country. You would need to look deeper into the history of both countries to see this; we do have a lot in common, the same problems with corruption and lack of respect to the rule of law. It just that the problems are worse in Haiti.

Now, to answer your question the main difference is in the openness of both countries to external influences (commerce and immigration). Haiti was founded after a slave rebellion and it was the first black republic anywhere in the world. It was isolated by the major powers and France in particular was vengeful with its former colony.

Due to this Haitians founded their nation in complete rejection of the previous system. No whites were allowed to own land and there was not a big incentive for the immigrants that settled in other countries in the area (such as Cuba or the Dominican Republic) to settle in Haiti.

In hindsight you could say that these policies were counterproductive, but who was there to assist the young nation and see that it was successful? Who was there to promote commerce and investment with Haiti? The major powers when they were not sabotaging Haiti were ignoring it. You can't really blame the Haitian if they developed an us against the world mentality that kept them close and in relative isolation.

The D.R. in contrast was more open, so much so that they even had one president in the 19th century (Ulises Heureaux) who was the son of an Haitian father; this happened in 1882 and the war for independence from Haiti ended in 1856. I think this has a lot to do with the relative success of the D.R. vs. Haiti.