Music in the Virgin Islands, both US and the BVI is both influenced by West Indian/Caribbean types; reggae, soca, calypso, cadance, zouk, steel pan... and also American music; rap, r-n-b, country.... you have both on both sets of islands. The majority is Caribbean however there is a lot of American music as well. There is traditional scrach band music on both islands, probally a little more on Tortola among the older population. Dancing - you wont find the quadrille or the bambola being the norm on either island - however there are dance groups that teach and promote the traditional dance and perform during festivals - this is true on both sets of islands. Mocko Jumbies you find in the USVI and to some extent as well during festivals in the Bristish islands- I would not say they are indigionous only to the BVIs no - they are found in other Caribbean islands as well - so is the music and dance. Masquearades that perform during Carnival are similar on both islands yes - and again similar to what is found on other Caribbean islands. The factors that you have discussed are what I would consider more part of the West Indian tradition of all the Caribbean islands; from St. Martin to St. Kitts, to Trinidad... these music types and dance types, food although not mentioned in your post and other cultural characteristics that you inquired about.... are historically part of an African cultural background combined with other cultures but realistically speaking - is really a West Indian Culture, A Caribbean Culture, unique to the islands. And it can be appreciated in both the British Virgin Islands are the US VIrgin Islands, as it can be appreciated as well in other Caribbean Islands as well. However it must be noted that the BVI's and the USVI fly American and British flags respectively and thus they are heavily influenced by the cultures of those countries.
No one drives horse and buggies or donkeys to travel - on St. Thomas people drive Jeep Liberties, BMW, Fords, Lexus, Mercedes... you get the picture. You can see donkies in the wild on St. John - on St. Thomas you can see them either in a few people yards, during the Agriculture fair or being paraded around for tourist to take picture with. No donkeys for travel though - thats not been the case for quite a few years, quite a few!
I am not sure I have answered your question. If you are looking for an island where African traditions - traditional African tradtions are practiced without the influence of other cultures, not sure you will find that.
Overall you will find that music, food, dance is quite similar on both sets of islands - in my opionion this is becuase the islands are both Caribbean Islands with a strong West Indian influence. However both sets of islands are very different in the atmosphere - this difference is created because of the difference in 'mother countries' American vs. British.
Please post again if your question is not answered, or if my answer created more questions. Have a good weekend.