I'm not an expert on Classic Doctor Who, but I've gotten the impression that most of the companions back then just left and/or were abandoned by the Doctor – we've seen at least four of them show up in post-reboot Who, after all, and they all seemed relatively fine other than an overdeveloped sense of adventure. Compare that to the fates of nuWho Companions:
- Rose Tyler: got trapped on a parallel Earth (although later with a human clone of 10, so not all bad).
- Martha Jones: left of her own accord and joined UNIT. Good for her!
- Donna Noble: Got Time Lord-ified and had to be mindwiped by the Doctor to save her life. Fixed in the 60th specials, but still.
- Amy Pond: got sent back in time by a Weeping Angel. Lived out her days with the love of her life, but still bitter-sweet.
- Clara Oswald: Killed by a time shade in the form of a raven, although the Doctor did some shenanigans to keep a zombie version around.
- Bill Potts: Got turned into a Cyberman.
- Graham O'Brien, Ryan Sinclair, Yasmeen Khan: left of their own accord. Good for them!
So, that's 5 out of 9 (or out of 7 if you count "the Fam" as a single collective) companions who suffered severe consequences for being companions. That's pretty rough.