Impact Resistant Glass
You don't have to close anything or put anything up. If you are building a house and haven't yet ordered windows, it might make sense to pay the extra money to install impact resistant glass.
The not so good?
Impact resistant glass retro-fitted is notoriously known for leaking and when it is replaced the old window has to be chipped out of the stucco and the stucco repair "never" quite matches. Keep in mind that impact resistant glass can still break. Its just glass with laminate in between. It also will scratch just like regular glass. Imagine having a house full of scratched impact resistant glass caused by a hurricane and having to replace it all. I highly do not recommend impact resistant glass unless you are building a new home with it, and even then, there are disadvantages.
Impact resistant glass will cost you a substantial amount more than accordion shutters. First they have to remove your present windows (usually they crush them to avoid as much damage to the wall as possible). Now they have to install the new glass. Many homes have expensive decorations on the walls that will have to be redone. Unless you have an older home and need to replace your windows anyway, the downside often exceeds the upside.
True impact resistant glass windows have a layer of actual glass, a center of polycarbonate, and an inner layer of glass. Beware of monolithic impact glass, this is a Lexan single layer in an aluminum frame. Sometimes people create opaque windows by washing them with Bonami (an abrasive window cleaner) or a solvent. What happens if an object strikes an impact glass window during a hurricane? It may shatter the outer glass glazing (like a car windshield) but the wind and water are kept out.
Building codes for impact glass are 140 miles an hour and the large missile impact test. Accordion shutters depend on the engineering and manufacture but for less than ten feet tall, they handle winds over 180 miles an hour...