The Norse and German traditions do not describe the same Brynhild. In the Poetic Edda and the Volsunga Saga she is a valkyrie who disobeyed Odin and was punished with mortality and marriage, later drugged with a potion of forgetting that explains why she can be tricked into marrying Gunnar instead of the man she truly loved, Sigurd, a detail that gives her later grief and revenge a specific mechanical cause within the story.
The Middle High German Nibelungenlied has no valkyrie backstory at all: its Brunhild is a superhumanly strong queen of Iceland who can only be won through a contest of feats, and she is deceived rather than magically drugged, discovering the trick only after the marriage. These are not variant details at the edges of one story but different premises about who the character fundamentally is and why she acts as she does, which is exactly what comparative scholars use the two traditions for, treating the difference as a record of how a shared legendary figure was reshaped to fit two distinct literary cultures centuries apart, Norse mythological narrative on one side and German courtly epic on the other, rather than treating either version as the correct one and the other as a corruption of it.