The British Virgin Islands are a British territory, with the governor appointed by the British Monarch. The assembly is elected locally. It has a constitution which went into effect in 2007.
Yes, you are correct. Generally, I have found the former British colonies are better than the French/Dutch/Spanish.
Although I have never been to St Barts because it is too expensive.
Yet, Jamaica is one of the most screwed up islands and it is/was British.
The Caymans is the richest per capita island because of off shore banking. It is also the island where the seasonal help makes the most money. I was there about twenty years ago. Almost everyone working there was Canadian because the Cayman dollar was 2X the Loonie.