That's it right there. It's not Babcock's style per say, it's the team he has to work with, or the situation he's in. I don't think he looks our current roster, with McDavid coming in, and says "Oh yeah, we'll put a trap system in and win the cup". No matter where he ends up, he will coach that team to their strengths. That's what a good coach does (See Dallas Eakins) he doesn't try to pound the proverbial square peg in to the round hole.
Though I'd be thrilled with either McCLellan or Babcock. I would be disappointed with Nelson. Sorry boys, he didn't set the world on fire prior to coming here, he didn't win 'championships' in OKC, and the Oilers still played like crap under him (look at the 8 - 2 loss to LA, the twisting in the wind LB was in that loss to San Jose, and losing to Vcr's AHL team in the last game of the reg season). Now, granted, we had a lot of injuries ourselves true. But, I didn't see anything spectacular from him either.
Nope, not in this off season, DeBoer, Carlyle, Crawford, potentially Hitchcock and Julien, plus the aforementioned Babcock and McClellan, no way Nelson should be our next HC.
Let him go back to Bakersfield I say. Finish off his coaching contract.