In grammar I was taught that smarter than I was the correct way to say it or write it.
But to me that just doesn't sound right and when you say or write smarter than me it sounds and reads much better.
So although I was taught in grammar that smarter than I was the correct way to say or write it I always would go with smarter than me.
Are you smarter than me? Are you smarter than I?
See what I mean the smarter than me sounds and reads better.