They'll also do this if they get it in and find damage preventing just a screen replacement after they've quoted you.^^^This.
Go with Apple. You'll get an OEM replacement part and won't have to worry.
Sometimes you may get lucky too. I cracked the screen on my 6+ over a year ago and because of the issues Apple had around the release of iOS 9 Apple replaced my phone for the price of the screen repair.
With the other (nightmarish) alternative being that the accidental damage to the phone is so great that a new screen can't be applied and one is stuck with paying the out of warranty replacement cost of $299+tax. Unlikely, but still possible.They'll also do this if they get it in and find damage preventing just a screen replacement after they've quoted you.
Prepare for the worst, hope for the best.With the other (nightmarish) alternative being that the accidental damage to the phone is so great that a new screen can't be applied and one is stuck with paying the out of warranty replacement cost of $299+tax. Unlikely, but still possible.