It's good that you're addressing this because even if her brother isn't smarter than she is, someone will be!
Have you tried asking her a hypothetical question: What would happen if someone (or her brother) is smarter than she is? Maybe you will get to the root of her anxiety that way.
When my son compares himself to his older sister and says things like "I'm stupid! I'm no good at <fill in the blank>" We talk about how being smart is not the same as knowing everything. That being smart is more about how a person learns things. Also, that everyone can learn things, and people learn different things at different rates. We try to emphasize that if a person wants to be good at something, that is going to take effort and practice whether that person is "smart" or not.
And of course, we try to remind him that we love him whether or not he is smart.
As a mother of a child who is a perfectionist, with at least one possible overexcitability, we use this same approach which works WONDERS!!! DS5 is so super sensitive and will start the whole "nobody loves me, everybody hates me, I'm going to eat a worm" thing at the drop of a hat if DD3 proves to be just slightly better than him at something (or anyone else for that matter). And reminding him of the above really helps a lot!
