Unless you can do everything by ear, you need both.
I have seen a classically-trained woodwind player utterly frozen and bewildered in a session where there were no dots.
My own approach is a mix - harmonica mostly by ear, not necessarily accurately. Melodeon by dots to get at least melody, some of the timing, but have tried the big slow session by ear at Towersey, and playing by ear seems less impossible. Ancient East German Anglo treated as subset of melodeon - it helped when I worked out that it seems to be in G/D, not a dreadfully out-if-tune G/C. Guitar by listening and guesswork in a session, but dots or sometimes tab otherwise.
Voice by ear, but dots were given the other day and came in handy.
To quote Rollo Woods, there are three secrets to playing music:
Quote from Lester Simpson that only when you are heartily sick of practising something are you ready to play it and play with it.
Be interested to hear how people may have got on with DVDs - I know John Kirkpatrick has done one for the melodeon.