I don't think they'll take Upshaw for the exact same concerns you mentioned. He's not versatile enough, think his upside is a poor man's Brian Thomas. Would be fine on the second day, but I want somebody who can be more in the first round. You never know until draft day though.
Rich Cimini recently updated his list of players he thinks the Jets might take at #16. He's been money the last few years and his lists of 5 or 6 guys have always included the guy the Jets have taken. This year's most recent list has Quinton Coples, Mark Barron, Dontari Poe, Courtney Upshaw, and Michael Floyd. It's an interesting list to me because you've got two guys who are major boom or bust prospects (Coples, Poe), one guy with a low ceiling high floor who doesn't appear to be a good fit (Upshaw), and two guys who kind of make sense but seem likely to be off the board (Barron, Floyd).
Cimini also mentions that he thinks they plan on taking the best defensive player available, and tosses out that the six that he thinks they'd like are Claiborne, Cox, Kuechly, Ingram, Poe, and Coples. The reason he lists Poe and Coples on the list instead of the other four is that he thinks those are the two who are most likely to be on the board at 16. He also manages to slip in Whitney Mercilus and mention that they've shown recent interest in him, so his 5 person list really mentions 10 players, though of all of them Claiborne is basically a lock not to be available and I think Cox is close to it as well. Certainly seems like they'll stick to their prior BPA strategy, although i'm not huge on the boom or bust guys. It'll be interesting to see what his final list looks like.