Like Dean without Sam is a completely different person, (in this case if he never had a brother, though we will get to sibling relationships when one goes missing or dies too.) Like He probably wouldn't be as protective, He would probably stand up to John because he wouldn't have gotten yelled at for being a kid and needing space from his annoying little brother and having adult responsibilities put on him.

Sam without Dean has no one to check his anger. He would be vicious, a lot closer to soulless Sam, but without the excuse of being soulless. Not that it would make things better, and he's still capable of empathy, but it doesn't come out as much, because he only knows one type of love.

Now, in a scenario where they did grow up together, such as in the show, Dean without Sam is a Mama Bear with someone between her and her cub. It's a predator hunting his prey. He's a self sacrificing octopus mom who doesn't eat and ultimately dies to give her eggs their best chance (not all octopi, but some). Dean without Sam is a wolf with Rabies, vicious, lashing out at everything, and ultimately needing to be put down because he's a danger to himself and others. And if he can't be one of those things, or after he's tried all those things and they didn't work, he is a shell of a human being. Going through the motions in the hope that someone or something will take him out, and end his miserable existence. (Lot of Bark, Strong Bite, but doesn't last long)

Sam without Dean, is all Bite. He loses all warning, all sense of morality. Dean is his anchor. Without that anchor, he embraces the storm of the sea. instead of running from it he becomes it.