the neck nailbomb is bright as $%&#
I believe the neck diver is a bit brighter than the cold sweat
The Holydiver neck is definitely brighter than the Cold Sweat neck and lower output, too.
The neck HD isn't far off a vintage-spec pickup, as I understand it, although I don't know what type of wire it uses.
I'm always surprised when people say the Cold Sweat neck is bright. I don't find that at all, although I've only tried it in mahogany, set-neck guitars. It will sound brighter in a guitar with a bolt-on maple neck, but not very bright.
So..... I haven't answered your question, I don't know the HD or NB neck models, all I'm saying is I wouldn't worry about the CS being too bright.
I think the neck diver is pretty close to an underwound cold sweat, 42.5 awg poly wire and symmetrical coils, if I my memory serves me well
the neck cold sweat has served me well in most guitars I had it, but they all were mahogany bodied gibsons and gibson copies
it is brightish, but not in a thin/trebly way by any means, and definitely not TOO bright
in the bridge, the neck sweat is almost as bright as a riff raff, but middier and more articulate, so yes, I'd say it is a bright pickup
neck nailbomb was the brightest neck humbucker I've ever played
quite scooped as well