I'd agree that Krueger and Nelson were more collaborative coaches and Eakins and McLellan are more stubborn coaches. Both Eakins and McLellan are open to some feedback though, I know Eakins had grand plans about a training regimen he was going to implement, but he wised up pretty quickly to how grueling the NHL travel schedule is for West Coast teams relative to what he was used to in the AHL. Eakins is hands down the most stubborn coach I've come across and I don't see McLellan being that head strong. As far as who those two listen to I think both McLellan and Eakins are more a fan of the leadership group relaying to them what changes they want and ignoring the rank and file players who aren't part of that group. I think McLellan prefers to get most critical feedback from his assistand/associate coaches, every coach who's worked with him seems to only have great things to say about him and it seems to be a collaborative environment on the coaching staff side of things, the only thing I've heard to the contrary is Gregor stirring up that Manny V. wasn't getting enough input into the PP. For McLellan right now I'd say McDavid, RNH, Russell, Larsson, and Lucic likely have his ear anytime they want it, in Eakins time it seemed he always had time for Ference and Hall.
Hall was very strong headed and was quite resistant to coaching input, I do think being traded though was a bit of a wake-up call to him, which likely made Hynes job easier, getting him to change. Given the vast amount of coaches we had in Hall's time here, being a bit head strong was probably in his best interests if he changed his style for every single one of them, he might of lost sight of what made him such a great player. If Hall was still here I'm sure McLellan would be open to listening to what he had to say, he was the top end of the roster, not some bottom of the rung utility forward; heck Hall and Eberle both were in favor of having McLellan hired after they got a chance to play for him.
I know he said Renney was the scariest of his coaches when it came to making a mistake and getting chewed out for it. Krueger is an all together nice guy that everyone enjoyed having around, but I think he was one of the group that took issue with how he was handling Yak with kid gloves, not forcing him to the same defensive standard. While the other players didn't like it seems like that was the best path for Yak though, he played so much better after he scored and had some confidence, he is one of those players that needed to learn how to score with regularity and then circle back to learn how to play D after, though it's always a hard thing to manage when you hit such a player with reality, they might not catch on even after you sunk the time into allowing them to score at the expense of defense. Many coaches wouldn't allow Yak the freedom that Krueger did, preferring to set a singular standard for team unity and accountability, plus building that standard into the team culture, opposed to taking a varied approach for individual player development.
Almost all the players hated Eakins, but I think Hall was a bit indifferent, Eakins was trying to crack the corsi code and translate that into NHL wins, Hall was driving his corsi results so was rarely in Eakins crosshairs (water bottle gate aside) and got a lot of autonomy. I got no idea who Halls favorite Oiler coach was, but I'd hazard a guess McLellan was in his top 3, likely Nelson in there as well he seemed pretty happy playing for him in the AHL during the lockout.
