Enough time has passed to evaluate the effect of Bill Belichick's cheating. The cheating took place from 2000-2006, and was ended early in 2007, giving 5 years of data since.
The known cheating consisted of two components, as revealed by Eric Mangini. First, the Patriots would tape opponents defensive hand signals. This permitted coaches to correlate the signals with the defensive alignments and figure out what each signal meant. Second, the Patriots used unregistered radio frequencies, so that the second time they played that team the offensive coordinator could watch the defensive signals and choose the perfect play to tell the quarterback. Normally, the referee cuts the registered radio frequency 15 seconds before the snap, so the offensive coordinator cannot communicate with the quarterback after the defense makes its substitutions, but the Patriots were the only team in the league that had radio equipment that could broadcast on multiple frequencies simultaneously. After the referee would cut the registered frequency, the quarterback could still hear the coordinator on the other frequency, so he could be told the defensive alignment he was facing and what play to call.
So the plays and blocking schemes were always perfect ones to exploit each defensive alignment.