It's an interesting question that will be endlessly debated with no clear answers likely to emerge.
It's pretty clear at this point that Murphy, sucking the air out of the room in the press conference, controlled the LaFleur hiring process and made the final call. We can safely say the McCarthy firing was his call as well. The Murphy-Gutekunst dynamic, or lets make it Murphy-Gutekunst-Ball-LeFluer dynamic as that evolves, is going to be hard to ferret out without being in the room. And what it is now may not be what it is 6 months from now.
Did Gutekunst pound the table on the LaFleur hiring, leading Murphy to the ultimate decision, while strenuously objecting to others with Murphy listening? Or is Murphy like the bosses some of us have had that make it clear where our lane is without actually drawing the lines, whereby you're forced to go along to get along while picking spots to steer the boss becomes a delicate process. At least Gutekunst talked about winning a championship whereas Murphy talked about getting back to "winning" ways which we might happily take as Gutekunst's endorsement. Maybe. There's that go along to get along thing if that's what the boss requires.
So, at the one level of firing and hiring a head coach, I think it is fair to say Murphy was the decider. Back benching Thompson? Obviously Murhpy.
At the level of all those formerly drafted players that were picked up for injury replacements this season (2018 draft 2.0 as I call it), the choice of those particular players would have been Gutekunst's working the old scouting reports and recent tape. McCarthy may have had input into particular needs at the moment, but that should not have been subject to much debate.
In the middle, between HC firing/hiring and picking up bottom of the roster guys, there is vast middle ground. How far down will Murphy reach? We may never know. He has taken the bull by the horns in a Kraft-like way (trade Garoppolo, make nice with Brady's personal trainer, and other some such). But in the keep-or-cut Perry decision, to take just one example, is Murphy going to dip down that far in making the call or will he say, "you 3 guys work it out." Is he going to sit in the draft room and weigh in on the #12 pick as it approaches or come up with his list and avoid the room, or butt out altogether?
I'd like to think the line gets drawn at those kinds of Perry/pick decisions, roster construction and cap management, below the level of jumbo contracts. While Gutekunst keeps his thoughts close to the vest, Murphy has a newfound chattiness with respect to football operations that has been building over the last year. He may give us some clues as to where he draws the line. Maybe.