There's been one or two historical surveys of that; in general, British colonies did better than French or Spanish. (Is that beause the British grabbed the better colonies? Well, Spain was the big power long before Britain had much of an empire, so if that was the issue, you'd expect Spanish colonies to do the best.)

To me, the institutions and culture of the colonizing agents were extremely important. Spanish colonies were led by representatives of the Crown and the Church, both very hierarchical, top-down institutions with little appreciation for dissent (or a good suggestion). British colonies were led by a variety of malcontents, fortune seekers, and utopianists, and in most cases Britain was only too happy to see them leave and remain a good distance away. They came without a lot of direct oversight, and a combination of circumstances (e.g., Jamestown) and principle (e.g., Plymouth Colony) led them to develop more egalitarian, meritocratic institutions. But it should be noted that many of the fortune seekers in Virginia and the southern colonies *intended* on pursuing the same extractive approach of the Spanish colonies but geology and climate worked against them: not much gold or silver on the Eastern Seaboard and too cold for sugar (although indigo, rice, and tobacco were plantation crops where it was warm enough and wet enough). The Spanish approach was not sustainable in most of the territory claimed by the British. However, where the climate *did* cooperate, such as in Barbados and Jamaica, British colonists tended to follow the same extractive model as the Spanish with largely the same long-term results. It is interesting to note that those British colonies that pursued the extractive model are today the states that exhibit the same patterns of poverty and low educational attainment, relative to the rest of the United States, as the former Spanish colonies used as examples in the video.