The only real difference in the construction of featherbeds and fiber beds is the filling material. Both appear to be a thick pad that goes on top of a regular mattress. The filling of a featherbed is feathers and down, usually from geese. The filling of a fiber bed is a synthetic product designed to provide similar levels of comfort.
One of the downsides to a featherbed is that over time it often loses some of its feathers. A bed filled with feathers includes many with small, sharp spines that poke through the bed's material over time. They are sharp and uncomfortable, and slowly but surely the filling escapes from your bed topper. This is not a concern with a fiber-filled product.
Featherbeds have been a luxury item for hundreds of years, and they are still more expensive than their synthetic equivalents. The price of a featherbed depends on what types of feathers it has as stuffing; high-grade feathers and down from specific types of birds command higher prices. White goose down is typically the most expensive and is regarded as the best type of down.
Because featherbeds are made from a natural product, they trigger allergies in some people. Very sensitive people can have an allergic reaction even to a featherbed labeled hypoallergenic. Allergies are not usually a problem with fiber beds. However, both fiber beds and featherbeds provide a haven for dust mites, and many people mistake allergies to dust mites for an allergy to the bed itself. Use a washable cover for a feather or fiber bed to keep out dust mites.