Personally if this ever comes up for me, i would probably allow a dice app for large damage (Fireball, lightning bold, high amounts of sneak attack).
This way i know it will be at least somewhat random but will actually speed up combat because we wont have to spend the time counting up the multitude of dice!
However i would want all other dice to be rolled with real physical dice.
Of course for online play I prefer people to use the built in dice roller, as everyone is using the same dice roller the issue becomes a moot point...
as the DM will gain the benefit of any non randomness as much as the players so it evens out.