I don't like Woody as an owner but it is wrong to infer that he does not give the team the money to compete. Pace, Harris, Scott, Revis, and Cro were all given top dollar contracts. Likewise, Sanchez, Holmes, Mangold, Dbrick were all given top 5 contracts.
His fault is when he puts the business side ahead of the football side. On things like hard knocks, Tebow, Farve, ESPN camping with the jets -that type of crap.
The problem with the jets is Tanny's fault. He spent future dollars and traded up all the time and filled out the roster with Big name FA. Pace, Scott, Cro (yes I know he was traded in the last year of his contract) Faneca and one year rentals.
His caving into Rex and picking Defensive players in both the draft and FA
leaves the team with no cap space next year and needing to replace 1/2 the defense in one year while the offense struggles to get out of their way.
Rex is who he is, he is brash and entertaining and has proved he can have a very good D when he has very good players. This year he doesn't, whether he should be replaced should be based on how well he adapts the D to compensate for the lack of Revis.
The jets are suffering from some play that can be placed at his feet, a lack of urgency and toughness.
I think Rex can succeed but he needs a complementary coaching staff that he does not have at this time, and with Westhof leaving it does not look any better going forward.