In Of Mice and Men, both chapters 1 and 6 begin with descriptions of the landscape of the Salinas River. In Chapter 1, it is evening; in Chapter 2, it is afternoon. The novel ends where it began. This represents a cycle of behavior. George and Lennie would work a job. Lennie would get into some trouble. Then they would regroup at some location (in this case, the Salinas) and plan to find work elsewhere, somewhere they are not known.
In Chapter 1, Lennie and George are together. The first thing George says is to tell Lennie not to drink so much water. This is a fitting opening statement because George is frustrated and angry with Lennie but is also just trying to protect him.
In Chapter 6, at the beginning, Lennie is alone. This is the crucial difference. He didn't forget that George had told him to hide in the bush if something went wrong. Like in Chapter 1, Lennie is tentative but then dunks his head in and drinks a lot of water. Again, frustrated but protective, but this time George concludes he must do something more drastic than a scolding.
From there, the differences continue. Lennie imagines being scolded by Aunt Clara, presumably because George is not there to scold him. And of course, this would not be a rest stop en route to their next job because George realizes that Lennie's well-intentioned but destructive behavior has to stop. More personally for George, he doesn't want Lennie to have to deal with Curly and/or the law.
The main similarity is the setting. The main difference is the situation, and this is somewhat foreboding in Chapter 6. In Chapter 1, George and Lennie are together and in Chapter 6, they are apart. Also, notice that in both Chapters, when Lennie and George (in Chapter 6, just Lennie) approach the water, all the animals (including the rabbits) rush for cover. This is symbolic of the dream of their farm (with the rabbits) running away from them. In Chapter 1, this dream is temporarily elusive, unlikely, but still a faint glimmer of hope. In Chapter 6, it is finally realized as impossible with Lennie's death.