The big difference is no one would ever question Brees' ability to read and process the field even with San Diego. Sure, he might not have been a for sure future HOFer at the time, but he ability to progress was always there.
This game showed a significant flaw in Taysom's game that's always been there that we were looking to see if there was progression. His ability to understand, process, and attack zone defenses. Atlanta attacked him with man most of the game (C1/C3) and the Saints responded with lots of man beaters and simple reads. This game Denver attacked with zone and Hill was frozen on the pond.
Now, just like one game didn't make him (ATL game was great), one game doesn't break him (DEN was terrible) but stats don't go down into why a QB was bad. Hill cannot be a long term successful answer if he doesn't fix what caused him to fail against Denver.