Here’s the deal, Sam has yet to consciously recognize that Dean doesn’t want to hunt anymore than he does.
In the episode, “What is and What Should Never Be” (2×20) Dean is drugged up a Dijinn and dreams of an alternative reality where his mother never died, Sammy stayed at Stanford, he’s monogamous and overall, never had to hunt, got a real childhood.That’s his dream world, the one that he could never expect as reality because (to use a phrase supernatural uses a a lot) “good things don’t happen to us”. Besides in the end, he realizes and snaps himself out of his dream world because all the people he saved weren’t saved in his alter world and realizes how many people could die without his help.
In 3×10 “Dream a Little Me” the episode where they end up in their nightmare world to try and save Bobby from a student who used to never dream until he was given some African dream root. Dean’s dream begins with Lisa and him having a picnic, that they’ve got to rush in order to pick up Ben. Sam is surprised, and Dean lies, “I’ve never had this dream before.”
By 6×21 “Let it Bleed” (When Dean was happiest at the beginning of Season 6) Dean ends up ditching Lisa and Ben, by having Castiel erase their memories of him, so they aren’t hurt. Sam doesn’t approve and Dean tells him to never mention them again. He takes the pain on his own. By 6×21 “The Man Who Knew Too Much” Castiel, (Dean’s main confidant and only known living friend) has gulped the Leviathan down to become God, and dies before Dean can do anything. (7×01)
Dean goes straight to killing Leviathans while dealing with and taking care of a Broken Sammy, (Who he fyi, died to get to chat with Death in order to try and get his soul back for, who he made a deal with a crossroads demon for, who he went to hell for.) Has his father-figure (Bobby) killed due in part by his best friend’s actions. He finally successfully cleans up Castiel’s mess, and is sent to fight in purgatory for a year for it.
Let’s give Sam the benefit of the doubt here, and say, he doesn’t know what happened to his brother, or Castiel. His psuedo-mother figure (Bobby) is dead, and overall he’s alone in this world. That’s tough. Most people in those situations, go back to what they know, which for Sam is hunting. He hits a dog, stays in town to get dog treated and falls in love with a girl whose husband died. So he ditches hunting. Sam is just allowing the world to take him where it pleases.
Then, his Brother who has literally died for him twice, comes back, he ditches the girl to go fight.
Considering, that he finally got his “normal” world, it’s a big sacrifice. When he comes back, he emulates Dean (pretty much his patriarchal figure) and suffers in silence until he’s pushed enough that he admits it, bit by bit. Dean however, whose entire life has been sacrifice, (only curtailed by frisky women, drinking in bars, eating hamburgers and pie, and his short almost marital bliss with Lisa) does not understand why for once, Sam couldn’t sacrifice himself to save Dean for once. Not knowing that Sam did sacrifice for him, by ditching the girl, all that he tells Dean on this is, “Then there wasn’t a girl”… Dean isn’t even aware of the depth of his feelings.
When things come to a head in 8×06 “Southern Comfort” when Sam faults Dean for killing his friend Amy for being a monster when he’s friends with a monster and even states that he’s going to be the one to kill Benny when things go wrong. However, Sam doesn’t realize that he spilled Dean’s own blood when he killed Dean’s daughter in 7×13 “Slice Girls” in Dean’s eyes, just because she was a monster. On top of that, Dean’s guilt at bringing an outsider into the supernatural world (New family, or a monogamous relationship) wouldn’t have applied with Emma, because she started out that way.
Dean has also developed a strict sins-committed before killing things prior to this. After he killed Amy Pond, her son came in, and he asked if he had killed any, and when he said he hadn’t but he was going to kill him. He walked off and let the kid live. Same with the Shape-shifter Baby in 6×02 “Two and a Half Men”. Emma, hadn’t committed any crime yet, so, Sam, basically killed Dean’s daughter in cold blood without knowing if she had actually become a monster (by killing anyone) and in this sense, Sam killed someone who was more innocent than his older brother (who had tortured souls in Hell, and has killed people).
By this, Sam and Dean now have differing ideas of what a monster is, and Benny doesn’t fit Dean’s.
Sam and Dean, have always desired the same thing, (Normal life without having to hunt, Dean: mainly with his family; Sam: where his potential maybe realized) Dean just hasn’t ran away from his responsibilities or the family curse. Dean has recognized that in knowing what he knows and having done what he has, he now has a responsibility to the world. While Sam, has felt a victim of circumstance, even when he was doing demon blood and started the apocalypse in “Lucifer Rising” 4×22, he was tricked by Ruby, the convenient scapegoat.
Sam has always considered himself a freak “After School Special” 4×13 because of what he knows and was consistently called it through the many schools they went to, fuel for the “victims of circumstance” arguement, he also resented his father for it, even after he learned to understand after what happened with Jessica. (Which was the yellow-eyed demon’s fault, and Sam not making a deal with Lilith was Dean’s fault).
Dean has continually been grateful for what he has had. He called his Dad a superhero, gave his brother the cereal he wanted, was glad to wear the samulet, had his mother murdered before his eyes at an age he could remember and only wanted revenge, furthermore when he almost died 2×01 “In My Time of Dying” he was going to let himself die. In “After School Special” 4×13, he considers himself a hero, and not a victim of circumstance. He is continually grateful that he gets to save people and considers him drinking, eating junk food, and sleeping with random chicks his reward.
Sam-hunting because of his brother making him, he’s the victim. Dean-hunting because he wants to save people and partly owes it due to what he did in Hell.
So basically their desires are the same, but because of the different ways they have interpreted the stuff that happened to them, it has made their worldview completely different and made Sam feel entitled to live a “normal life” while Dean’s worldview has made him feel responsible for others’ lives (Which one could argue is because of their roles as kids, Dean took care of Sam, while Sam just worried about his own life).