At least a public deposition would allow people to come to their own conclusion. If Chelsea felt that public questioning was one sided and a smear campaign then she could release a statement afterwards filling in the context and pointing out the other side of the story.

With a grand jury it is illegal to discuss anything, so a one sided smear campaign during a grand jury can lead to an indictment and Chelsea would have no opportunity to offer her side of the story without risking more jail time.