playa del duque
This lovely beach is located in Costa Adeje - to be more precise in one of the newest areas - next to the very posh Gran Hotel Bahía del Duque. It's a 700 metres long beach with calm waters and has some fine grey sand. There are changing cabins, toilets and you can rent sun beds and parasols. Moreover nearby there's a good selection of restaurants and bars.
playa de las Américas
Massive development reigns here, in playa de las Américas everything reminds you that you are a tourist and that you are there to 1) spend money 2) have fun. The beach is very long, with grey sands and lined with everything you might need to spend the day (and night).
I did not like it: built in the late 1960's, it shows its age and is too grey (read: too much concrete) to look pretty. There are several rows of establishments, pubs, souvenir shops, fish and chips places... just mention something that's NOT Spanish and you'll find it there. Another thing that you will not find is peace and quiet.
Equipment: Don't bring anything... everything you neec is on sale