how much of an advantage does white have over black
Depends on the level of the players. For all the patzers below 1600, it means absolutely nothing! Both sides make numerous blunders that who goes first doesn't matter.
You start reaching the expert and low master level and it starts becoming more significant. Reach the GM level and it becomes even more significant! That's because at the GM level, far fewer mistakes are made and the advantage White starts with is often kept for the duration of the game.