Cundiff was signed in July to compete with Nick Folk for kicking duties.
Carpenter, a 2009 Pro Bowler, was released by Miami (on August 15) and Arizona (August 25) this offseason.
The Jets were said to be interested in Carpenter when he was released by the Dolphins, so it makes sense they would be interested again. Carpenter is younger, but that's not always an advantage for kickers. Carpenter was good enough to receiver AFC ST player of the month (2008) and was sent to the Pro Bowl in 2009.
Nick Folk only hits 65% of his kicks when the weather goes below 40 degrees (thanks Bent!), so that might be one of the reasons the Jets are looking for a switch. Cold-weather kicking is key for a team like the Jets, but other than that, I don't know if Carpenter is appreciably better in field goals or on kickoffs.