The difference in this series is less about the coaches, than it is more about the players their respective GM's were able to give them to compete. It is clear from Babcock's statements after the game, that the personnel he had was not the personnel he wanted for this team. He even said on a number of occasions, that he was overruled by Holland on several decisions (one of which was most likely re-signing Quincey and not letting Ouellet play the season). So unless Holland gives Babcock control over those kinds of roster decisions, he will not re-sign. And I think, at this point, Holland's ego is too big to give Babcock that kind of authority over the roster.
Babcock even said it best when he said, "...we’ve been drafting good, we’ve been developing good, but we’ve been winning too much. That’s the facts.”
That had to be a jab at Holland for putting together teams that make the playoffs, but can't compete. And if Holland isn't ready to compete...then he will go elsewhere.
Ultimately, we will find out a bit of what Babcock thinks (even though he will likely not say anything concrete), in a couple days when he has his end of season press conference. I expect him to say that he will take a couple weeks with his family to think about what's best. With his dad dying I think it complicates things a bit more, in the short term, and that he will need some perspective and a bit of wooing from other teams before he ultimately decides what he wants.
Who knows...he might just be coach of the Oilers, when it's all said and done. He already has a relationship with Nicholson and Chiarelli.