Like others, I play by ear the stuff I know and have lead sheets for stuff I don't know. I can play "full sheet" but as I do this infrequently I find I've got rusty and tend to use the sheet music as a check to make sure my "by ear" version is still accurate!

I think you have to develop both. As mentioned already (and I can confirm this from personal experience) if you work purely by ear you can "miss" chords especially as the chords move away from "C Major" toward "C minor plus 9 and 11 with Bflat bass". Using sheet music can "teach" you chord and harmonic structures that you might not have met before; once you know what they sound like you become more able to "decode" songs you listen to. Certainly I have listened to a song on the radio that I learned yonks ago, and haven't heard for a while, and think "so thats what that chord is..." having played the wrong one for years!