Neither is correct. Say "he ran quicker than I did".

"He ran quicker than i did",but in speaking english people often "me"

You say: "He ran more quickly than I" or "He ran more quickly than I did". We often hear it like this: "Who was quicker, Sam or me?" Actually, you should ask "Who was quicker, Sam or I? You would say I was quicker, so you should ask "was it I"? You would not say "Me was quicker", so don't ask "was it me"?

Randy is tough but totally correct. However most people would use me in speech.