Back to the original question for a moment ...
Putting aside the "one game at a time" cliche, the first priority for any team is to win the division. The second priority is home field in the playoffs, and that is determined by a team's conference record.
In other words, the Dolphins game is at least two levels more important than the Saints game.
No, it's not, because the Saints game counts towards winning the division too. I don't mean to repeat myself, but let's not forget that overall record is the most important factor in winning the division.
You could go 10-6 and lose all of your division games and still win the division. And you could go 6-10 and win all your division games and not win the division.
Division games can mean more, yes, but all games count towards winning the division. Just some have additional tie-breakers. Had we beaten the Colts and Denver, non-divisional foes, we would have had the division locked up.
If we lose to NO and Miami wins next week, they'll gain a game on us. We'll only be a game ahead in the division and playing the Dolphins with first place on the line. Meanwhile, if we beat NO and Miami loses, we gain a game on them. And the match-up against the Dolphins doesn't decide first place. If we lose, we're still in first place in the division.
If we could only win one of the two games, yes, I agree, Miami would give us more tie-breakers so I'd want that win. But that doesn't mean the Saints game isn't important. And it doesn't mean we sacrifice one for the sake of the other.
The Saints game is the most important game of the season now, just like the Jets game was the most important game of the season last week. It's an opportunity to gain a game on the rest of the division. Why wait until the Miami game to do it?