I am younger than...:
formal - 저는/제가 ~보다 (더) 젊습니다/젊어요 or 어리습니다/어려요
informal - 나는/내가 ~보다 (더) 젊어/어려
I am older than...:
formal - 저는 ~보다 (더) 나이가 많습니다/많아요.
informal - 나는 ~보다 (더) 나이가 많아.
더 is optional, and if you wanted to mention exactly how much older or younger you are, just add the number of years + 살 in place of 나이가 , i.e. 난 너보다 두 살 많다. - I am two years older than you. You can also say ~보다 + difference in years + 살 위여요/위여 to say someone is older.