I'm assuming you're referring to the situation when hiring a car. Although some countries do insist on both plastic and paper licences (such as Northern Ireland, where we go every August), in Tenerife, I've only ever had to provide my plastic licence.
I generally use my site's recommended company, Europcar, but have had occasion to use other firms when Europcar had no vehicles available (my fault for not booking online). Each time, my plastic licence has been sufficient.
If you want to make doubly sure, why not take your paper licence anyway, just to be on the safe side?