When we first see Donna, in The Runaway Bride, she's very shallow and small minded and when The Doctor offers her a chance to see the universe, she turns him down because she's not ready for that. (Although she does have an interest in seeing the world.)
The next time we see her, in Partners in Crime, she's changed. She's opened up and wants to explore the world and universe. She's so eager to go with The Doctor that she has suitcases all packed and ready and she carries them around for when she meets him. She's on to the Adipose situation and figures it out just as quickly as The Doctor does. She could never have done that before The Runaway Bride, where her experiences opened her to the wonders of the universe.
She had plans, she wanted to spend her life travelling with The Doctor and the two of them got along fantastically, in large part because she had no romantic interest in him and she was, as The Doctor said in The End of Time, his best friend.
And, at the end of Journey's End, she's expanded to the point where her brain can't contain all of what she has become. She's gone from blind to what's around her and only interested in a husband who has money and a position to beyond the horizon of her aspirations. She is ready to continue exploring the entire universe, and then she realizes it's all being taken from her.
The expanded Donna Noble is not only dead, but knew she was about to lose everything she had become. The expanded Donna did face her own ending or death. That consciousness, that personality, that self awareness that spend the time in the tardis with The Doctor is gone. While she is not dead, the expanded Donna Noble might as well be.
Then we see her one last time and she's small and petty again. She's making fun of her friends and talking behind their back.
Think of it this way: Suppose you had worked and studied to learn any particular field, and in that field you had achieved greatness and just as you are awarded the Nobel Prize for hard work and brilliance, someone shoots you in the head and when you get out of the hospital, you have no memory of all you had achieved and if anyone ever told you about what you had done, it would cause you to have a stroke or something, so you spend the rest of your life as far less than you were. The "you" that won the Nobel Prize has lost all chance of pursuing all the dreams you had and for the rest of your life you're stuck cleaning and doing lube jobs on robots for the Sirius Cybernetics Corporation.
Would you like having that happen to you and losing all you had achieved and losing all that you had become?