I think him being point position as John's hunting partner would've made him more likely to run away. Sam ran because he saw where John's revenge quest would land -- his entire family killed. The more hunting he did, the more he saw of John becoming monstrous through the act of killing monsters, the more he'd want to flee the life as quickly as possible.
Dean didn't understand why Sam left, which is why they had this exchange in the Pilot
DEAN: So what are you gonna do? You're just gonna live some normal, apple pie life? Is that it?
SAM: No. Not normal. Safe.
It was not about having a normal life, but having a life where he wouldn't watch his family members die in front of him. With Dean being younger than him, he'd be more protective of Dean and more worried about Dean being killed, which would give him extra drive to get out of the life ASAP.
At the age of 14, Dean would be considered old enough to start hunting with the other two, and that would be another driving factor. Sam would worry about leaving Dean behind, because he knew Dean would become John's point man, as Sam had been at that age (or younger), but Sam would leave for Dean.
At 18, Sam would feel old enough to set up his own household and try to convince Dean to join him. He'd use his scholarship money and stolen funds to rent a small two bedroom apartment and try to convince Dean to come live with him.
Dean would refuse, saying that John needs them. Sam wouldn't press the issue at first because he would assume that, without Sam there, Dean would come to see what Sam saw: John's quest would get them killed.
He would think that Dean is only loyal to John because he's young and inexperienced. He would think it was because Dean was so lonely stuck behind at home all those years. He'd think that in a year, at the very most, of hunting with dad and seeing the blood, death, and violence, Dean would come live with him at Stanford. But Dean wouldn't. Dean would be bitter about Sam 'abandoning' him and dad, even though Sam did his best to keep in touch and beg Dean to join him in safety. Dean would feel more of a sense of betrayal and the rift between them would be greater.
