Island Hoods vs Downdraft Ranges
Island hoods are four sided and affixed to the ceiling instead of a wall. They are designed to be used over an island in the middle of the room (hence the name). Back in the dark ages, when I was selling appliances, island hoods were clearly the worst category. Best seller in 1986, the Broan "Chuck Wagon" hood, followed by an equally awful Nutone hood. Imagine trying to sell that to a client with a contemporary kitchen.
I couldn't. We sold downdrafts instead. Downdrafts are a good aesthetic option, but not as good for ventilation. Smoke is normally captured in the plenum of a hood, but there is no capture area in a downdraft. Also, smoke travels up, so the downdrafts must work twice as hard with liitle or no capture area. However, for most cooking, downdrafts are still functional.
In the mid 1990s, island hoods became more popular, because of an influx of European imports. The new hoods were both beautiful and functional in gleaming stainless steel. A hood really handles large volumes of steam and grease better than a downdraft.
Island Hoods vs Downdrafts
The answer is as much about aesthetics as function. The downdraft disappears in the cabinet whereas the island hood becomes a design element in your kitchen. Functionally, there is no contest. The island hood is designed for any type of cooking, even professional (with the suitable hood). Downdrafts are not manufactured for that type of volume.
So the decision is based on how much you cook and the aesthetics of what you like to see.
For more information about terms, features and how to size a hood , read the Yale Ventilation Buyers Guide.