I have chartered with CYOA in CA the past three years. I have also chartered (once) from Sunsail on Tortola before that.
I have not chartered from Island Yachts out of Red Hook but most of what I mention below should apply to them as well.

Advantages:
1. For me - cheaper air travel
2. Avoid the ferry hassle and can control my schedule to make my flight with little fear that the ferries are going to blow up, sink, or be delayed (ok... the first two are an exaggeration but the latter is not) and leave me with too little time to catch my flight. Which results in stress that I would just be happy not to have on vacation.
3. Better/cheaper provisioning
4. Better boat (better equipped) for slightly cheaper than the same sized boat from Sunsail (or similar)
5. In my opinion the boats are better maintained and cared for

Disadvantages:

1. CYOA has no chase boat. I don't know about IYC. I have not needed anything that would require a service call but boats are boats and it could certainly be an issue.
2. As someone has already mentioned - you need an extra day or day and a half if your intent is to be sailing in the BVI in order to get in/out of the USVI. Solution to that is to enjoy the US side - it's really pretty nice.
3. More limited boat availability. CYOA has been adding Cats and seem to be decreasing mono hulls which is probably a reflection of the market. From what I can see, CYOA has more dock/mooring space. I'm not going to pretend to know anything about their business, but I"m still going to venture a guess that if there were greater demand there would me more boat options - they seem to understand capitalism.

That's my experience. As they say... your mileage might vary depending on what you value.