The clue here is that schumacher was roughly as fast during the race, as hamilton was during the race. You do have to put that somewhat in perspective though: back then refueling was allowed, so naturally in 2004 between race laptimes and qualy laptimes was alot less. The qualy time back then was 1:28.351.
Suprisingly, the qualy time this year is 0.7s faster then back in 2011. Even though f1 got slower in a timespan of almost 10 years, they rebounded from the ban on EBDs, to go that much faster within the timespan of 2 years.