Both leave from Los Gigantes harbour and both put you under the cliffs. The difference is how much effort you put in and what you want to see.
Kayak: closeness and effort
You go at water level, right along the base of the cliff, often combined with a swim or snorkel. It is a physical activity and very wind-dependent, and the wind on this coast picks up around midday: early departures find calmer water. Not the choice with small children or if you want comfort.
Boat: distance, whales and calm
It covers more coast with less effort and is the way to watch cetaceans, which live year-round in the channel between Tenerife and La Gomera. It often works better with children or reduced mobility, though comfort against seasickness depends on the size of the boat and the sea. Whale watching is regulated by the Canary Islands Government, which requires authorisation and a minimum distance of 60 metres from the animals; a good operator keeps to it.
Which one fits you
You want to see whales or dolphins
Boat. The kayak does not reach the channel where they are.
Small children, or someone prone to seasickness
Boat: steadier and effort-free.
You want contact with the water and you are fit
Kayak, and book the early slot before the wind sets in.
Either way, check the day’s sea state before booking.