Be the Better Example
It might seem like the best idea is to avoid that competitive mom; just stay away and you won't have to deal with it. However, that may not a realistic solution. This is your time to be a better example.
Don't feed into a competitive mom's behavior and comments; instead, offer something positive in return. If you demonstrate a pleasant attitude and speak only encouraging, kind words, she will probably take note of that. She may notice that you get further along when you are patient and demonstrate integrity.
Keep Things in Perspective
Remember to keep things in perspective. Sure, your friend's child may have potty-trained earlier, but in the grand scheme of things, it really won't make a difference. Many of the things that parents are so focused on in the here-and-now seem so important, but in later life really won't matter.
If you can keep things in perspective, you can keep your wits about you when you are around a competitive mom.
Share Your Feelings
What if the competitive mom is a friend? That can change things a bit. If your friend is competitive and you find the conversations are constantly about how great her kids are, you might share your feelings with your friend. Be honest about the way her behavior and comments make you feel.
Sometimes, competitive moms are not even aware of the way they are acting. They may not realize how they are coming across to others and could end up thanking you for pointing it out.