L.,
That is one ugly little world, isn't it? The unfortunate truth is, there's nothing any of us can do to stop jealousy. You can try talking to the girl's Mom, but I doubt it will do any good, and it will be very hard to phrase what you are trying to get across without this other woman taking it as though you are saying "gee, sorry my daughter is better than yours, but oh well, they should be friends anyway." Of course, that's not your meaning, but a jealous person can take almost anything and twist it.
To answer the question of what I would do, truthfully, I'd get my little girl way far away from that whole scene. I've heard a lot of stories like this, where children who are successful with these pageants are treated badly by the other kids, or the other parents. Being made to feel bad for winning is no way to teach a child to strive to be the best they can be. Personally, I have concerns about teaching a little girl that her success or value lies with how pretty she is, or what she wears. Our society does enough of that. BUT, this is my personal opinion of children's pageants, I don't have a child who participates in them, and never have. EVERY parent has the right to make these decisions for themselves and their children, and I certainly do not judge or criticize if you think differently.
Are there other outlets for her that would give her the same enjoyment without exposing her to this kind of competitive, jealous environment? Does she enjoy dance classes? Or perhaps a children's theatre program? These would give her the opportunity to get dressed up, be on the stage, and enjoy all of that, without the element of competition and all of the negativity that it brings. Again, just an idea thrown out if you are looking to change what you are doing. If you decide to keep with pageants, please just do your very best to shield her from those comments and those people who would make her feel baadly about winning. That's no ghood for her self esteem. If she's "throwing" contests at 5 years old, the message that it's bad to win is getting through.
Jess