Perhaps surprisingly, flights are not necessarily the fastest way to travel between islands. Certainly they are if you want to go to Santa Cruz de Tenerife: there are 17 flights a day, and they take about 30 minutes.
But if you want to go from one small island to another, say La Palma to El Hierro, then that means two flights. By the time you’ve checked in, flown to Tenerife, waited for your connection and flown again, it can easily take four hours.
The Armas ferry takes four hours, and it costs €12.50 one way, instead of about €41.70 (and that’s a special offer). The catch is there’s only one direct ferry a week, on Sunday afternoon.
If you’re going to Gomera, it’ll take you four hours to fly, and only two on the Fred Olsen ferry or three on the cheaper Armas ferry.
Most inter-island flights to Tenerife go to the north airport (Los Rodeos, TFN) whereas the ferries go to Los Cristianos in the south, which is near the international airport (Reina Sofia, TFS).
Mostly, it boils down to what’s going in the right direction at the right time, and whether you want to take a car.
Oh, and for people who suffer from travel sickness, the usual tablets are Biodramine.
Ferries
Fred Olsen Fast (2 1/2 hours) ferry to Los Cristianos in southern Tenerife
Naviera Armas ferries Slower and cheaper. Also the only direct ferry to El Hierro.
Trasmediterranea Ferries to S/C de Tenerife, Las Palmas de Gran Canaria, Arecife and Cadiz
Flights
Binter Canarias Inter-island flights
Islas Airways Inter-island flights (website in Spanish only, but usually a little cheaper)