During the Brady era, the thing that I have noticed the most distinguishing the Patriots offenses from the Bills is what seems to me to be a vastly different approach to offensive game management. The Bills approach always seems to be that you have 3 downs to gain 10 yards cumulatively. The Patriots approach seems to be that you have 3 chances to get 10 yards on any one of the three chances. Of course this mostly comes down to having Tom Brady. And the Patriots go three and out plenty. But it seems as though the Patriots approach leaves the defenses guessing a lot more. Playing calling seems far less situational for Patriots than the Bills, and therefore less predictable, which in turn makes it hard for defenses to defend.
Said another way the Bills have "passing downs" and "running downs". Defenses play to the predictability. The Patriots play calling seems far less predictable.
I am not in anyway comparing Allen's talent to Brady's. One is unknown, one may very well be the GOAT. However I do feel that Allen's skill set will allow an OC to be far less predictable in game management that we have been in the recent past.