"Corroborate" is extremely formal in tone. If your goal is to sound natural, I would suggest: The security cameras back up her story, not yours.

Number (1) sounds more natural than number (2). "Corroborate" means to confirm or give support to (in this case, it would mean confirming or giving support to the statement). Number (2) sounds awkward. "More corroborated" is not used, just like "more confirmed" is not really used. "That of yours" also sounds a bit more formal than just saying "yours." For example, "The security cameras corroborated her statement more than yours" means the same thing and sounds more natural. As a final side note, "corroborate" is a little higher on the formal scale than "confirm." You might hear this word, "corroborate," in formal situations, like the court room.

Another problem with ‘corroborate’ is that it doesn’t fit with your ‘more of’. Natural would be: Security camera video corroborates her version of events. To capture the ‘more of’ nuance, you’d have to say something like: Security camera video corroborates some portions of her story that differ from yours. (Clarifying that it doesn’t corroborate her entire story, but that it makes her appear more accurate)

2