I've been a music teacher for 10 years, a pianist for 26 years (professionally for the last 14 of those), and a mom for 4 years. Here's my answer:
I would tell her to get over herself. There will always be people who do things better than her. Sometimes it will be her own brother. I would tell her to be happy for people (even her own brother) who excel in something and that she needs to find joy in doing things simply because she likes to do them, not because she's the best at dong them.
I would, as a mother, stand up for my younger son who doesn't deserve to feel guilty about being good at something. This is a really exciting time for him and he deserves to have praise. Make sure you take him aside and explain that, even though big sister is causing drama, YOU are proud of him and YOU will stand up for him and make her stop.
Their future happiness as adults is at stake here - I mean that. In just 10 years SHE will lose a job for whining, crying and carrying on over someone doing something better than her. Not to mention how much that attitude will stress her out (obviously since she cried for several straight hours last night!) And HE could end up being that person who constantly gets passed over for promotions because they sit quietly while others take the credit. Or the person who has a great idea that goes unnoticed because someone else doesn't think it would work.
She is 10 and just a year away from the frightening world of middle school and it sounds like this attitude/outlook on life has been going on for awhile. I believe we need to parent based on the "big picture" instead of focusing on the tears and drama going on at the moment. Look ahead a bit and realize that this behavior will NOT serve her well and will more than likely get her bullied. I've been a middle school teacher for 10 years and the kids that do really well are the ones who have been taught appropriate humility (in her case) and pride (in his case) and when it's okay to have those emotions.
If you're wondering how to start this dialog, try this. Does she like a sport? Does she still play that sport even though there are other people who get paid millions of dollars to play that sport better than she does? Of course she does because it's fun to play! Same thing with piano.
Best of luck turning that drama train around. It's never fun to put one child in their place while building the other one up, but it will be worth it for each of them separately AND for their sibling relationship in the long run.