For Provo:
I think it is like many of the islands in the Caribbean, it all depends on where and how you stay. You can arrange a quiet relatively inexpensive stay that is not "touristy" or you can stay at a big expensive resort full of people that will have a more touristy feel. It is no more expensive than GC and can be just as or less touristy again depending on where you stay.
The diving is expensive, much more so than say a Bon or Cur but comparable to say a GC. The diving is excellent.
There are no cruise ships visiting Provo which is a plus if you are looking to assess a "touristy" index.
Very true, we like Grand Cayman but we stay in a more residential and less touristy area and not on Seven Mile Beach or George Town - and we avoid the most popular attractions during peak days/times for cruise ship visitors.
You have to be willing to rent a car and do some driving on the left side of the road if you stay "off the beaten path" on many British islands but there is a lot more traffic on GC then on Provo in the developed areas - and traffic on Nassau, too.
One of the reasons we like Turtle Nest Inn on GC is because a rental car is included in the price and it is centrally located so we have access to various districts on the island and if you go toward the East End there is isn't much traffic - but again - it isn't the best choice for a heavily dive-focused vacation - or even a short, weekend getaway - I think Sunset House would be a better choice for a weekend trip to Grand Cayman. OP, you may see some Reef and Nurse Sharks around GC, but you are more likely to encounter sharks around Provo and Nassau (and parts of Florida).
Both Provo and GC have beautiful beaches, but I think that Grace Bay Beach on Provo is the widest and prettiest of the 2 beaches and the color of the water is astonishing! Keep in mind that Provo and the T&Cs suffered extensive hurricane damage last year, but reports indicate that the rebuilding is going well.
I don't know if this situation has gotten better or worse lately, but there were some rather alarming reports of robberies and even violence against tourists on Provo last year before the hurricanes - so if you stay in a remote area, be sure that it has good security systems and be careful venturing out at night; see below. You can be a victim of crime any place in the world, including your own neighborhood, it is just something to keep in mind. Of the 3 choices mentioned (Provo, Nassau, and Grand Cayman) I think that GC is the safest destination - but none of them are really bad.
Security Message for U.S. Citizens: Turks & Caicos, Violent Armed Robberies in Providenciales
Security Message for U.S. Citizens: Turks & Caicos, Violent Armed Robberies in Providenciales
Burglary; Assault
Western Hemisphere > Bahamas
7/31/2017
The U.S. Embassy in Nassau advises U.S. citizens residing in and traveling to Providenciales, Turks and Caicos, to be aware of their surroundings and remain on heightened alert to avoid being a victim of crime. An increase in armed robbery, including violence against victims, remains a threat facing U.S. citizens in the Turks and Caicos. In the past year, a number of U.S. citizens have fallen victim to armed home invasions while in hotel rooms and private homes, as well as armed robbery while walking after dark. Two U.S. citizen victims were shot and seriously injured.
Review your personal security plans; remain aware of your surroundings, including while attending local events; avoid walking on roads and beaches after dark and monitor local news stations for updates. Maintain a high level of vigilance and take appropriate steps to enhance your personal security.
Due to the surgical limitations of hospitals in Turks and Caicos, emergency care frequently requires medical evacuation to the United States. Check in advance with your insurance company that your health insurance covers the cost of medical evacuation to the United States, or obtain traveler’s insurance that offers such coverage.
If you are the victim of a crime abroad (including the loss or theft of a U.S. passport), you should immediately contact the local police (dial “911” or “999”) and obtain a police report. Contact with the Embassy should be made as soon as possible thereafter.