Should Dolphins Prefer Carr or Rodgers for Jets?

The Miami Dolphins pretty clearly are going to be facing somebody other than Joe Flacco or Zach Wilson when they face the New York Jets in 2023, but who should they and their fans prefer to see join their AFC East rivals?
Aaron Rodgers and Derek Carr are the two big names associated with the Jets early in the offseason, based on reports they have engaged with the Green Bay Packers in trade discussions and they entertained Carr on a free agent visit this weekend.
From a practical standpoint, maybe it's better for the Dolphins if the Jets get Rodgers because that would require them to give away draft compensation, where they can simply sign Carr now that he's been released by the Las Vegas Raiders.
Neither Rodgers nor Carr is coming off an impressive 2022 performance, evidenced by their finish in the league passer ratings of 16th and 24th, respectively.
With Davante Adams in Las Vegas instead of Green Bay and with NFL rushing leader Josh Jacobs, it also can be argued that Carr had the much better supporting cast as well, proving more evidence that if we're looking strictly at 2023, Rodgers figures to be the better quarterback.
If we're looking from a long-range view, Carr would make more sense for the Jets given that Rodgers' Hall of Fame career is winding down and Carr will turn 32 in late March.
THE DOLPHINS AGAINST DEREK CARR AND AARON RODGERS
Looking strictly in terms of how the Dolphins have fared against both QBs, the numbers actually are pretty similar for both Carr and Rodgers.
The Dolphins are 3-2 against Carr, who has a 92.6 passer rating with an average of 302.9 yards per game against Miami but six touchdowns and five interceptions.
Miami is 1-3 against Rodgers, who has a 92.9 passer rating. He's averaged only 253.5 passing yards against the Dolphins, but his TD-INT numbers are much better at 7-2.
The Dolphins have won five of their past six against the Jets, including the 11-6 victory in the 2022 season finale that put them in the playoffs.
The one QB who beat them was Zach Wilson, the 2021 second overall pick whose days as a starter in New York appear to be finished. In the finale, the Dolphins made life miserable for veteran Joe Flacco, but he really didn't have much of a chance behind a porous and injury-riddled offensive line.
The Jets are going to have to address that offensive line regardless of who plays quarterback for them next season, but they certainly should represent a bigger challenge for the Dolphins and the rest of the AFC East if they land either Rodgers or Carr.
For 2023 alone, the Dolphins should prefer Carr be the guy; if it's Rodgers, they probably wouldn't have to deal with him very long.
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