Schumacher was only faster in "race speed", well no he wasn faster in "race speed", he only has more fastested laps than Hamilton and this can be easily explained, because he had different rules. He made almost all his fastest laps, when his car was much lighter than the others, because he had less fuel and then he pushed.
In general I think the "concept" to distinguish into "race speed" and "qualifying speed" is pure bullshit!
Either you have "the speed" or you don have it. It is just that some drivers have a different approach for the weekend of the race. So they have a different focus. Schumacher was very tactical, so he and Ross Brawn thought about the perfect amount of fuel for the race.
So letś just say "speed" and here I see both Hamilton & Schumacher on one level.
It is anyway impossible to say who was the "fastest", as different areas have different cars, rules etc.
I also see absolutely no problem concerning tyres with Hamilton. He has five world titles now, so this obviously is no problem.
I really cannot rank drivers, like I could rank Boxers, as too much depends on the car.

Science says Fangio is the best formula one driver ever and on rank number one. Schumacher before his comeback is on rank 3 and after his battle with Rosberg he is only on position 8 in the list:
https://sputniknews.com/world/2016041610...ula-one-driver/

However I also would not totally agree with this list! However Fangio should be always mentioned when it comes to the best ever. He won his titles with many different teams!