While the history of the Caribbean is not my primary area of expertise, I do have enough background knowledge to offer an educated answer. I have also listed my sources at the bottom of this post, which of course go into much more detail than I do. It is also worth mentioning that Haiti was not always poorer than the DR. Until the 80s, Haiti was more wealthy by most metrics, which indicates that some of the causes for its poverty are relatively recent.

A question like this is always going to be much too complex and multifaceted to give any concrete answer. That being said, there are certain factors and historical events that have certainly contributed to Haiti's poverty.

The obvious example is, of course, the dictatorship under Duvalier. Due to his human rights abuses, most of Haiti's wealthy class fled to the US, Canada, France, and Francophone Africa. This contributed to the current poverty in two ways. First, as the wealthy owned most of the wealth (by definition), this wealth left with them. Second, the wealthy tended to be educated, meaning that nearly all of Haiti's doctors, engineers, scientists, etc no longer live in the country. With such a lack of educated people, it was considerably more difficult to rebound after Baby Doc's reign ended. It is worth mentioning that the Dominican Republic also had a period of dictatorship under Trujillo. However, he emphasized the importance of education (similarly to Cuba under the Castros), so while there were many problems under his rule, a brain drain was not a significant one (at least, not compared to Haiti).

We also have to consider the colonial histories of these two countries. As you may know, Haiti earned its independence through a slave revolt. It was only the second country in the Americas to earn its independence (after the US). As such, many European powers, including France, Spain, and Britain, feared the precedent. These nations didn't want Haiti to become a successful and wealthy country full of former slaves, as that would have sent a message to slaves in other colonies that a revolution for independence would increase their quality of life. Thus, there was a European boycott of Haitian goods, and this lack of trade began Haiti's transition from a relatively wealthy country (by the standards of the Americas) to a poor one. To make matters worse for the Haitians, France agreed to recognize Haiti's sovereignty only after they pay a debt of 150 million francs in compensation for French​ losses during the revolution. This debt was paid over eight decades and was only fully paid off in 1922. Due to the interest on the 150 million, the Haitian government ended up paying much, much more to their former colonial owners, which did not help the financial situation. These were problems that the DR, which became independent much later, did not have to face.

These grand historical reasons aside, there are also many smaller contributing factors as well, including the difference in tourism, which is a huge component of the economies of almost all Caribbean nations. This is where poverty becomes a sort of positive feedback loop. Because of Haiti's poverty (and resultant insecurity and social violence), it is not a popular tourist destination, so it lacks many funds that the DR enjoys.

I hope I've answered your question to a satisfactory degree. As promised, here are the sources I used (forgive my formatting, I'm on mobile):

1. Why the Cocks Fight: Dominicans, Haitians, and the Struggle for Hispaniola by Michele Wucker

2. The Imagined Island: History, Identity, and Utopia in Hispaniola by Pedro San Miguel

I did not use this work in my response, but it's worth a read if you're interested in the topic (though it can be quite dry): The Old Regime and the Haitian Revolution by Malick Ghachem.

Question re the premise...is Haiti actually worse off (economically?) and by what measures?

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