I have to give the nod to 0-16 definitely.
The record NFL losing streak is 26 games (the good 'ol expansion Bucs) while the record winning streak is 21 (playoffs and combined) by the Patriots/18 in the regular season.
There are a number of good reasons:
Teams will generally bring their best to play an undefeated team and try to make a statement (the Bengals were below .500 in Marvin's first year when they won Chad's guarantee game of then-undefeated Kansas City).
Injuries will have a greater impact on a great team than a bad one. Would the Colts go 16-0 if they had to play 8 of the games with Jim Sorgi at QB? Not likely. Bad teams, however, don't magically have good players drop from the sky to rescue them and the quality of players is bad enough that oftentimes even if they play an injury-plague team, that team's backups are superior to their starters (Sorgi could realistically fight for the #1 job in Oakland).
While teams often will let down against bad teams (hell, the Texans beat the Colts twice last year), the equation changes when that bad team is winless. While the winless players have professional pride, so do the guys who don't want to lose to the 0-fers.
Resting for the playoffs definitely can impact the late season games for an undefeated team, making them more likely to lose. If a team is winless, however, they might be willing to take a chance with unproven players for the future at the expense of current season wins.
-QG