The paradigm offered is an interesting one. I think that the difference between both visions of reality is that "man vs. machine" reflects what the reality is and the idea of "sane individual vs. crazy institution" is a reflection of what reality should be seen as. The collision and difference between the two is that one vision shows how reality should be seen and the other is how it actually is perceived to be. The difference between both visions is how reality is constructed.
McMurphy, and later Chief, embody the idea of how reality can actually be "sane individual vs. crazy institution." In this configuration, the individual is actually more attune to reality and is willing to speak out regarding such a condition. As a result, the institution feels compelled to silence such a voice at all costs. Bromden understands this is how Nurse Ratched appropriates reality. While she is a part of the "crazy institution," she does everything in her power to ensure that the individual who knows themselves to be "sane" is silenced by any means necessary. The institution's interests are served by removing the voice of the sane. The dynamic in the condition of "sane individual and crazy institution" is that the individual knows that the "system is out of order" and that they are the lone voice of "reason" in a configuration that seeks to silence them.
The implications of this condition is one in which the individual who is actually "sane" becomes appropriated as part of the "insane institution's" machine. Essentially, Kesey shows this dynamic to be how the "insane institution" is able to maintain and consolidate its power. It is for this reason that Nurse Ratched runs her ward as a machine, something that Chief points out early in the narrative:
The big nurse tends to get real put out if something keeps her outfit from running like a smooth, accurate, precision-made machine. The slightest thing messy or out of kilter or in the way ties her into a little white knot of tight-smiled fury. She walks around with that same doll smile crimped between her chin and her nose and that same calm whir coming from her eyes, but down inside of her she's tense as steel. I know, I can feel it. And she don't relax a hair till she gets the nuisance attended to—what she calls "adjusted to surroundings.
Kesey uses the appeal to a "precision- made machine" as a part of the condition in which the "insane institution" is able to silence the voice of the "sane individual." In seeking to dehumanize the individual, making them part of a machine of "precision" and efficiency, the "sane individual" is silenced. The use of lobotomies is one way in which Kesey shows how the voice of the individual is silenced by the prowess of the machine. Kesey's work is able to depict the reality of "man vs. machine" is a result of how the "insane institution" is able to crush the will and silence the voice of the "sane individual."