The Jets interest in Finley is in no way at odds with any desire to bring back Jeff Cumberland. Cumby has established himself as a good second option, but there is a gap if they want more production out of him.
Finley had a neck injury that will keep teams from investing much into him and it has recently been reported that the former Packer is "close" to getting his medical clearances. While some teams might be squeamish, the Jets experience with Kellen Winslow Jr. might make them bolder than most. Finley is by far the best player in a mediocre class of free agent tight ends, so would be worth a serious run thanks to the Jets more than generous cap space.
Either way, both moves don't preclude them from still drafting a long-term solution in the mid rounds. Cumberland and Finley can provide value here and now while a mid-round draftee will take a little time in acclimating to the NFL game.