I was leaning more towards Dave's arguments and then he clinched it with the Tolkien references.
Parcells won two Super Bowls with just above average QBs and teams that were more solid than star-studded.
His coaching tree is one of the most impressive in football.
He coached in a great division against other great teams/coaches and during a time when there was no shortage of great teams.
He resurrected numerous programs in short order.
Was Parcells perfect? No one is but Parcells is rightfully a first-ballot HOFer.
To the original question, I doubt that Parcells would have matched Belichick's feats but New England would have remained the strong program he turned them into.
Also I disagree with Fig's take.
1) Cheating is a cardinal sin
2) The margin between victory and defeat in the NFL is razor thin. In the years the Cheatriots*** were cheating (Belichick admitted under oath that he had been taping opponents signals since he took over New England in 2000), they won numerous close regular season games which made their road to the Super Bowl much easier. For instance, in their first Super Bowl season they won 4 games by 3 points or less.
Their 3 Super Bowl victories were by a total of 8 points. I won't digress into a discussion of the Tuck Game and all those ramifications.
You will never convince me nor do you make a strong case that their cheating was not instrumental to their success.