The differences between the successes of north and south America has been explored by economists. One significant factor was the lack of property rights of south Americans. Basically traditional serfdom was exported to south America, whereas the people in the north were able to buy and own their land allowing them to become independently wealthy. Those in the south had to pass nearly all their wealth to the landlords.

There are also other factors like the dominant protestant work ethic in the north (i.e. that working hard is the best way to get close to God, as opposed to focusing on observing dogmatic traditions).

There was also a more established rule of law in the north and there are other differences. So although the potential for similar outcomes was there at the start when the Americas was being founded, they set off on wildly different trajectories.

Edit: I'd recommend reading Civilization by Niall Ferguson.