My glass cracked on my own Xperia Z3 - the actual LCD was in perfect condition, but after the crack, only half of the digitizer touch surface worked.
I had the digitizer replaced and it worked well for a while, but then it broke again, and I had the whole screen replaced.
That was a bad idea - the replacement screen is trash, poor colors, poor brightness, overheats, drains battery and unfortunately only lasted 2 weeks before it broke permanently.
Unless you're sure you can get a genuine original LCD, don't replace the screen.