I have a mad work schedule and sleep disorder, so I'm up as well!
Goodness, this is a tough one, @OP. For one thing, your DS (who sounds like a positively lovely boy! well done you, raising such a mature and caring young man!) likely would worry quite a bit about his SF (sad friend), and for quite a while. I'm well on in years and even my DC are grown, but I often think of, and worry about, and have even tried to find, one particularly sad girl I remember from year 3!
And, I know this is NOT your problem and NOT your responsibility, but looking at it from the outside, I might worry about SF as well. If he talks about dying, and he's only got your DS as a friend... Goodness, that's so sad. But from a mum's perspective, I'd worry about DS's reaction to 'leaving him behind' as he may see it. He could feel guilty and even find it difficult to enjoy having a good time at the new school if he worries about his poor SF still there and suffering.
Perhaps you could speak to the school about what DS has told you about SF, some of the things he's repeated to you, about the way the particularly mean boy treats him? It's all things your son has relayed to you himself, so I don't think that would be a breach of privacy...? [However, somebody more well versed in these things, please do say if that's incorrect!] You could let them know that there is one boy who is often especially mean to SF, and that he's talked about dying, just so that somebody is looking out for the poor lad. That could help ease your DS's mind about the move, and make him feel less guilty about switching schools.
Maybe even if you don't do the move; that's really an awful lot of heavy responsibility that your lovely boy has taken on as it is. Hmm... would it be possible to meet with SF's parents and ask if they could move him to the other school as well? Maybe after DS has settled in and shown to be happier? You could broach the subject knowing both your DS had trouble with some of the boys in class.
But in reality, just as you said, it's your own DS's future you've got to concentrate on, and just as you said, you cannot let this other boy's situation dictate your son's future, even if DS might feel bad about it for a while. It does sound like DS would be much happier, and therefore do much better, at the other school. From what I've read here, I think I would do the move, if I were you.
Maybe you can sit DS down and talk to him about all of that, even though it's a bit weighty? He sounds quite mature, so maybe you can just lay it all out for him. Explain to him how much it would impact so many other aspects of his life, being happy at school - how there would be more social opportunities in and out of school, how he would be happier in general. The school years really seem like forever at his age; that's several more years of going to the same school with the same social group every single day. Perhaps suggest he arrange some activities with his friend, and ensure him that they can and will keep in touch and remain friends. You could even ask him how he would feel about you speaking to the head teacher or something, getting somebody to look out for SF, and you could ask his opinion on suggesting SF move to the new school after a term or so.
Hehe, you've created a conundrum for yourself by raising such a lovely and sensitive DS. I don't envy you this difficult decision, but it does seem like a fairly good problem to have. ;) Doesn't make it easier to solve, though!
(And ughhhh sorry for such a long post!!)