Reading or Playing by Ear? Neither, I play by chords. I don�t like the term music theory because it suggests something that has not been proven. There are certain logical rules that chords follow. There is only one reason why chords adhere to the rules of the road; it sounds good. That�s it. No theory here. It just works that way. This logic allows you to discern patterns that make up harmony, melody, and rhythm. Knowing the rules that chords almost always follow allows me to do the playing by ear thing. After awhile, you will know the sound before you press the keys. For me playing by ear meant that I would have to know the rules and the chords inside out. Playing by ear is just using chords logically. Then again, the same thing could be said for sight reading. Yep, chords are involved in both reading and playing by ear. But it is the ear that is the closest distance between what I am playing and what the listener hears. Just try blaming the sheet music for it not "sounding right".
If you are wanting to play classical music then all bets are off. Scales is the name of the game in that arena. And that is the stage that most music teachers stand upon by tradition.
Floyd