Memorization provides us with knowledge of a qualitatively and physiologically different variety— you take the verse inside you and you know it at a deeper level than if you had simply read it off a screen. What you have in your heart is more easy to access and apply to your life in spontaneous situations. You won’t have to open the copy of it or turn on your mobile for that.
Quran holds so much wisdom in it that keeping it in your heart will make you a wise person as well.