The article made for an interesting read, but there are some holes in the argument that the two are "tied."
First of all, you can't say the fact that Parcells has never been fired gives him an edge, because as some other posters have already pointed out, he never stays at a job long enough to get fired. He reminds me of a guy I went to high school with who was obsessed with chasing girls - he would go after one, win her over, then pretty soon he'd dump her and start chasing another one. It was all about the chase, once he actually had her he lost interest. Parcells is the same way. He loves turning around dysfunctional franchises, but once they start accomplishing what he wanted them to accomplish he gets restless and decides he wants to retire. Granted, with the Giants he quit because of health reasons, but look at everywhere he's been since.
Second, you really can't hold it against Belichick for getting fired in Cleveland because by that point the whole franchise was in turmoil over the revelation of the move to Baltimore. Although he kept most of the other top football people (e.g. Ozzie Newsome) Modell decided that he needed a fresh start in Balty after the absolute s**t-storm that were his last two months in Cleveland. Further, we can all agree that BB had four losing seasons out of his five there (and like Parcells is fond of saying, "You are what you are"), but let's take a further look, shall we?
The salary cap and free agency began in 1993, Belichick's third year in Cleveland. So in his first two years, Belichick didn't have that much to work with, since Modell was deeply, deeply in debt on everything associated with the Browns and thus couldn't sign away big-name players. BB worked with what he had, which wasn't much. Then when free agency started, Modell took a big gamble by using the little credit he did have to sign Andre Rison.
By 1994 BB had turned things around some and got the team into the playoffs (where, as mentioned, he drubbed Big Bill's Pats in their only head-to-head playoff meeting.) The 1995 season started out with some promise, but the team tanked once the Baltimore thing leaked out.
Plus while all this was going on, Belichick was taking a beating from the media, who hated Modell and focused their rage on his head coach. It didn't help things when Belichick announced he was cutting the aging Bernie Kosar, either. The media raked him over the coals in Cleveland, which is why he's so tight-lipped to this day.
Then there's the issue of revamping bad teams. Admittedly Parcells is the master of doing more with less (the 9-7 '97 Jets were largely the same team that had gone 1-15 the year before) but when Belichick took over the Patriots, they weren't exactly Super Bowl caliber, either. The team was in rough shape due to the infamous personnel decisions of Bobby Grier and many of the team's better players had been signed away to... Parcells' Jets.
Both men are going to the Hall of Fame, but IMHO when you look at both their careers critically Belichick is by far the superior of the two.