One way to contrast the characters of Carlson and Candy is to look at how these two characters align (or fail to align) with an impersonal and absolutist business sensibility that has little room for sentiment or friendship and that entirely accepts the realities of a competitive economy.
To some extent we can say Of Mice and Men is interested in highlighting the values implicit in a commercial system that benefits from keeping laborers from unifying and developing real social bonds. We can take Candy and Carlson as representations of two sides of this issue. (The substance of these two characters indicates the values inherent in the perspectives on each side.)
Carlson aligns himself rather completely with the status quo. He is a skilled ranch hand and his specialization gives him a somewhat elevated position on the ranch compared to the common laborers.
"Practical and down to earth, [Carlson] focuses on actions and doesn’t notice people’s feelings" (eNotes).
Not only is Carlson unsentimental, as shown in his insistence that Candy's dog be put down (because it smells bad), but Carlson also sides with Curley in seeking Lennie's death at the end of the narrative.
Carlson does not possess the emotional sensitivity that Candy displays, as is made especially clear when he fails to understand why George would be bothered after he has had to shoot his only true friend.
Slim, a person with feelings, leads George away in the aftermath of the shooting while Curley and Carlson remain behind.
"Curley and Carlson looked after them. And Carlson said, 'Now what the hell ya suppose is eatin' them two guys?'"
The profound lack of understanding from Carlson shows him to be a character devoid of real emotion. What he possesses instead is a sense of self-interest that makes him similar to Curley, a figure also aligned with the status quo of life on the ranch that favors one class over another and that maintains divisions of class and race in the service of a discriminatory system of capital and labor.
In short, we can say that Carlson is a perfect fit in a competitive system in which he has an intrinsic advantage.
Candy, in contrast, is a figure who is at a disadvantage in this system. He is no longer capable of doing hard labor on the ranch and his status is thus diminished. His low position is demonstrated when his one real possession is taken from him—his dog.
Candy is not happy with the status quo, as we see when he excitedly involves himself in a plan to buy land with George and Lennie. He wants to change things. He wants to live in a system of cooperation, where the competition of his current life is replaced by partnership.
This economic philosophy is matched by Candy's social tendencies. He is friendly and cares enough about others to stand up for them, as he does when he defends Lennie from Curley's wife.
"'You let this guy alone. Don't you do no messin' around with him.'"
Candy's sense of connection and emotional understanding are in direct opposition to Carlson's self-interested perfunctory sensibility.