Classic makes it really clear that the Forsaken are different after being raised from the dead. They're the same person, but warmer, positive emotions are greatly muted, and the more negative emotions dominate. For example, Clarice Feldman was the wife of a paladin who went off to fight the Scourge. In life she both loved him and resented him for leaving her. In death, the love is muted, and the resentment magnified. There's another quest about a husband who's wife was killed by his best friend. He sends you to kill that friend, and keeps his hands to remind him of his revenge, but gives you his only momento of his wife, her ring.
Classic is pretty clear that this is normal for Forsaken, that it's just how they are.
In D&D terms, it's like their alignment takes one step towards Evil after being raised. Someone who was Lawful Good in life is Lawful Neutral in death. Neutral in life becomes Neutral Evil in death.
In Battle For Azeroth, on the other hand, this doesn't happen in most cases. There are 3 new Forsaken raised during the story: Amelia Stone, Thomas Zelling, and Derek Proudmoore. All three of them seem like the same person after being raised, and don't exhibit the change in emotions. Zelling in particular is deeply concerned about his family, and hurt when they reject him. A Classic-style Zelling would care about his family in an intellectual sense, and insist that the Horde carry out their agreement to take care of them. But he wouldn't seek to see them or bond with them.
There is one case where the newly-raised Forsaken behaves in the Classic-style: the Night Elf Wardens. They come back angry at the world and Elune. Ironically, I've seen more player complaints about the change in personality for the Wardens than for Zelling or Proudmoore.
It makes me wonder if I missed something in the story. A plot point where Forsaken resurrection was "fixed", and newly-made Forsaken started coming back with an unchanged personality.