It is easy to cite the disadvantages of a stayless rig. These would include a larger diameter mast which means that the mainsail is operating in a bigger turbulent zone behind the mast. This hurts windward performance and severly impacts light air performance. You have a higher center of gravity (especially with the aluminum masts used on the Hunters vs the Carbon Fiber masts used on other free standing rigs) which means less stability for a given weight. The larger diameter mast translates to more aerodynamic drag (although not as much as you might think since wire rigging actually has a surprising amount of drag). It is harder to keep a tight headstay again reducing pointing ability. The other problem with a sagging headstay is that it powers up the jib in a gust just when you really want to blade the jib out. While the Hunter Visions are a fractional rig, you loose the ability to precisely control twist which is one of the biggest advantages of a fractional rig. Carbon fiber unstayed rigs have been quite reliable over their lifespan but now that they are reaching 25 years in age we have just now started to have failures occuring. That compares pretty well with the useful life of stainless steel standing rigging but you can replace a lot of stainless steel rigging for the price of a new carbon fiber mast. No one expects aluminum freestanding rigs to last as long.
Then there is issues of weight distribution. A freestanding rig places more than double the side load forces at the deck level. To take these laods large internal structures are required. Properly designed this puts a lot of weight forward in the boat and high in the boat. Improperly designed this results in an area that will be prone to long term fatigue problems. This weight distribution also affects hull shape as the bow has to be more buoyant to support this much weight that far forward in the boat. Mure buoyant bows (fuller) are not as good in light air, going to weather or in a chop.
I really do not know of a single real advantage.