As with most things like this, Haiti's problems aren't due to just one thing. That said, the French and US governments did just about everything they could to ensure Haiti failed after its independence. The Southern-dominated pre-Civil War American administrations did it because they really didn't want anybody to see a nearby Black revolution overthrowing a White government and succeeding, and the French basically out of a sheer bloody minded spirit of
va te faire foutre. Like
@Flash said, Haiti's revolution was a horror show.
The Dom Rep should have been an equally failed state, and until very recently it was. Most of its history has been one
caudillo overthrowing another and coups as the preferred method of transferring power, interspersed with periodic invasions from other countries. Then in the late 80s-early 90s they essentially got exhausted with the whole thing, plus sugarcane (its main export) was no longer worth what it used to be, and the country switched over to a primarily service-oriented economy in the span of about ten years. Since then, everyone in the DR's discovered it's much more pleasant having an economy based on golf courses and beach resorts, than working in sugarcane fields while the two rival
El Jefe Maximo Supremo-wannabes of the month shoot at each other.
Haiti's basic problem is that it just doesn't really
have an economy. Its third of the island was never really great for agriculture, it doesn't have anything else worth exporting, and some profoundly boneheaded decisions by its leaders have made it even worse. The near complete lack of jobs, education, or social mobility means it's always a riot waiting to happen. As a result Haiti's never been stable enough to attract investors to switch over its economy like the other former plantation islands - to tourism, offshore banking, etc. The little bit of tourism money there is, is because the French will go on vacation anywhere.