CYOA has a great reputation and I used them prior to purchasing my yacht (Sea Tiger, which is based in TMM fleet.)
Obvious advantage of STT (CYOA) is no ferry. Draw back is spend a day (or 2) getting to/from BVI sailing ground... I consider that minor unless trip is short. Biggest drawback is on day 1, with seas being greatest just outside CA, your crew (especially novices) may be more prone to sea sickness. Also be cautious of days entering BVI re: customs overtime fees.

Advantages of cruising around St John and generally less crowded, but beautiful.

I am pretty sure CYOA has chase boats arranged for BVI (But many companies do not send chase boats to Anagada). . If you choose STT as your starting point, Capt Jay at CYOA will take good care of you.