This is right from the back page of Bowhunting World.
Advantages of Vanes:
- More weather resistent
- Easier to attach to shafts
- Quiter in brush and in flight
- Generaly more durable
- Less expensive than feathers
- More weight and less air resistance provides greater arrow energy and speed at longer ranges

Advantages of Feathers
- Larger surface area gives more air resistance and generaly greater arrow control
- More flexible: less likely to be knocked off course after striking bow components or branches
- Generaly considered more traditional and aesthetically pleasing
- Less weight gives greater arrow speed at shorter ranges.