Part of the reason I really like the thought of the Jets potentially going after Mathias Kiwanuka is the thought of what he could do with Rex Ryan. Kiwanuka has shown a lot of versatility through the years. He spent over half a year starting at linebacker in the 4-3 defense the Giants run and most of his career working at end. He has experience rushing while standing up. He has experience dropping into coverage. He has experience at playing with his hand on the ground. The Giants even moved him inside on some passing downs to use his quickness to try and overwhelm slower and less agile interior linemen.
Rex Ryan loves getting creative with guys to put them in favorable matchups. He had a linebacker by the name of Adalius Thomas he moved all around in Baltimore. The idea was to change things up frequently. One lineman might get used to playing Thomas and become more effective gaining experience every play over four quarters. Moving him around, though, consistently forced new blockers unused to facing a guy with his athleticism to take Adalius on. Thomas was a Pro Bowler under Ryan. He was something of a free agent bust for the Patriots, who used him more conventionally.
If Rex Ryan ever got his hands on the pass rusher, I think Kiwanuka would have real breakout potential.