This scene in Chapter 3 is a crucial incident of foreshadowing that makes George's act at the end of the novel all the poignant. The crucial difference between this scene and the end of the novel is that Candy does not kill the dog himself. Later on though he realises that he should have done it, which we can see impacts George greatly and is one of the reasons why he chooses to kill Lennie at the end.
Both Candy and the dog and George and Lennie have been together for a long time. Candy says he had "had him from a pup" and it is clear that Candy feels great attachment to his dog. Slim says "That dog ain't no good to himself. I wisht somebody'd shoot me if I got old an' a cripple" showing that the dog is not able to function in life now. In a similar way, Lennie, through his disability, is not able to function and fit in to life - we have already seen that through his attempt to pet a girl before. It is clear as well that the dog is completely dependent on Candy - just as Lennie is completely dependent on George.
The differences are that Candy's pup used to be the best sheepherder in town, whilst Lennie has always had his disability.