It's interesting to compare the DVOA rankings to the Sagarin rankings, since they're comprehensive formulas but with completely different considerations. The Sagarin rankings are based only on the results of the games (who wins, who loses and the scores), no matter what happens during them. The DVOA rankings are based only on what happens on each play during a game, no matter who wins or loses or what the final score is.
Since the Sagarin rankings are based on the full season, the best comparison is to use the DVOA full-season rankings instead of the overall rankings, which are weighted toward recent games. (It should be noted that the DVOA full-season rankings list two teams tied for 20th but no team 19th. I've changed that to two teams tied for 19th, since it's either that or a typo.)
As you can see, they're pretty similar for most teams -- 17 teams are within one spot in both rankings, and eight more are within two spots. The four biggest outliers (teams with the biggest difference in the rankings) are the Cowboys (10th in Sagarin, 14th in DVOA), Patriots (12th in Sagarin, 19th in DVOA), Rams (24th in Sagarin, 30th in DVOA) and Titans (30th in Sagarin, 25th in DVOA). But I have yet to pinpoint one particular reason why those teams' rankings can be so different using different methods, so it's probably a different reason for each team. The Cowboys, for example, might be better than their DVOA because they have the highest penalty margin in the league, and as far as I can tell, DVOA doesn't account for penalties.
Personally, I think combining the two rankings produces a more accurate ranking than either one on its own.