Competing against boss for same external job?

I currently work for a Fortune 500 company in management (recruited out of college 10 years ago) and was recently contacted by a larger company about a Senior/Executive level role. Pay is about 2-3x more than my current total compensation (300-400k total comp), however after some research it appears my boss may be going for the role as well. This would be a lateral move for her.

I feel good about it, and am qualified, but am curious how (if at all) I’m able to set myself apart from my boss if she truly ends up being my competition?

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