Katniss considers dying for her community while Peeta wants to die by himself.
Step-by-step explanation:
Peeta is an individualistic person while Katniss is the one who wants to represent her own society.
Thus, for her a death of dignity is one in which she dies by the side of the morals she has set for her and her people.
For Peeta it is less simple than that .
For him it is about the individuality of the person and he wants to stay true to himself first and foremost before anything else.
He is putting his own sense of morality above the rest.
If he compromises himself as in his ideas then he would have failed.