Franchise tag affixes a value that the Jets would then have to pay or at least put a longer term contract that the player would then sign in place to avoid the full tag price. That player can't negotiate with other teams without the Jets consent and would be compensated (generally draft picks) should a trade then take place. A transition tag is nothing more than a first right of refusal, and few teams ever use transition tags. As best I can tell, Max Starks of the Steelers in 2008 was the last time it was used in the NFL.
As for the Jets? The Jets might not have many players who might qualify as free agents who would be worth tagging, but if I had to choose a player or two to consider for the tag, it would have to be either Dustin Keller or LaRon Landry. Tagging LaRon would ensure that the Jets paid him $6.8 million for this season - probably more than the Jets would want to spend. On the other hand, paying Dustin Keller $5.9 million seems more probable. Of course the Jets have to wonder if they'd be bidding against themselves based on how 2012 went. Still, Keller had one of the league's highest catch rates (78%) of all Tight Ends in 2012, despite playing with the scattershot Mark Sanchez. Due to the injuries, Keller's production was severely limited. Keller is athletic and talented, but there might not be many teams lining up to give him a big contract once free agency begins -- but then again it only takes one.
Here's the projected franchise tag list and the costs associated with each position.
QuarterbackFranchise: $14.6 million
Transition: $12.8 million
Running backFranchise: $8.0 million
Transition: $6.8 million
Wide receiverFranchise: $10.3 million
Transition: $8.7 million
Tight endFranchise: $5.9 million
Transition: $5.1 million
Franchise: $9.6 million
Transition: $8.5 million
Defensive tackleFranchise: $8.3 million
Transition: $6.9 million
Defensive endFranchise: $10.9 million
Transition: $9.0 million
LinebackerFranchise: $9.4 million
Transition: $8.2 million
CornerbackFranchise: $10.6 million
Transition: $8.9 million
SafetyFranchise: $6.8 million
Transition: $5.9 million
Punters/KickersFranchise: $2.9 million