Both protect the opening. The difference is that impact windows are always working and shutters have to be closed.
Impact glass costs more and it is invisible. You install it once and forget it. Shutters cost a fraction and they are the right call on openings you are not ready to replace, as long as somebody is there to close them before a storm.
Plenty of Southwest Florida homes use both. Impact glass on the front where it shows, shutters on the back where speed and cost matter more. There is no single right answer, only the right mix for your house.