I am going to try to be objective with this subject.
There are several variables to consider in Byfuglien's value. Among them would be age, contract term, need, etc.
Byfuglien's greatest strengths are his abilities with the puck. He uses his frame to shield the puck probably better than any player. He can be an absolute force around the net. His shot is terrific, even his snappers come with a lot of power. He can stand up just up any player in the league.
Without the puck, his skating is his most obvious detriment. His cross overs look laborious, and he doesn't move his feet particularly well, unless going full steam. Conditioning is improved, but still prone to floating, though it seems he does so less as a forward.
When I look at the Jets roster he really seems to me like the most movable piece.
Enstrom is the QB on defense, Trouba is the most complete defenseman, Bogosian plays hard minutes, and the Jets look to have Clitsome, Postma, Ellerby, Redmond, and conceivably Pardy competing for jobs next year in the 5-8 slots. Maybe Stuart too, as a defensive leader, if the Jets and him are able to come to terms.
I think you have Kane-Scheifele-Wheeler as the top line for many years to come. Frolik has been added to Little-Ladd to make the line more defensively adept (only wish Frolik would take draws). If Buff can not crack either the top 4 d or top 6 forwards, and with a kid like Trouba who should surely supplant Buff as the 1st unit PP d-man, his greatest value is as a trading chip.
I look at a few teams who could surely use him.
1) Vancouver, with the Sedins he would be a force, the winger to give them space, maybe a 30 goal scorer. I think you could probably get Edler (who could replace Stuart's defensive minutes and be a 20+ minute a game d-man if Stuart isn't to be resigned) a young speedy Minnesota kid like Jordan Schroeder, and a 2nd rd pick are achievable, maybe Edler and Shinkaruk even, as Vancouver's window isn't forever.
2) St. Louis, L.A has physically dominated the Blues in the playoffs in consecutive years. A player like Buff would sure be a force on a line with Backes and Steen. I think reasonably you get Jaden Schwartz who would be a real asset on a 3rd line with a promising future ahead of him, Ian Cole (or Roman Polak, who is really needed as a RHD, unless Bogo was to move back to the left side) and/or a 1st. Jake Allen would be a good return to, but hard to see the Blues giving up on him, with Halak possibly leaving at the end of the year.
3) Tampa, flying under the radar all year, Buff would sure complement Stamkos and St. Louis better than Ryan Malone ever could. A lot of prospects on Tampa, from Vasilievsky to Killorn, could help us fill the cupboards.
4) Montreal, Dudley is in their organization, no team needs size more than the Habs--Eller, Tinordi, 2nd?
I think the trades involving Duchesne or Skinner are a little far fetched, those are going to be 40 goal scorers in their prime, and their value probably is straight up Kane, Scheifele, or Trouba. I prefer the proposals for a 3rd line young gun, who can move up the lineup, a top 4 d-man, and picks.
The position of the forward we should get in return will be influenced by the returns we get for Setoguchi, Jokinen (who I think should be resigned for 2 more), Stuart, and maybe Burmistrov.