It's difficult with people who truly want to have that contest. I'll be honest, when I posit an opinion/perspective that might be different than my friend's, I might mention something I have read, more to share information than anything else because I work in childcare and find the topic endlessly fascinating. I'm always learning, and like to share insights/helpful articles with friends. Using discretion means that I don't bring them up as an argument to a friend's position, but more as a "hey, did you read that? What did you think?" I'd say that, used this way, sharing information draws me closer to that other mother. Sometimes (a lot) moms need empathy, not another bit of advice. So I try to keep "are they asking for advice or just venting" in my mind for the moment.
I don't know if that is what your friend is feeling, or not-- competitiveness or a need to justify herself because she's still finding her way or feels challenged that you are doing things differently than she is. I do know that there is a whole culture of judgment/strong opinions on different aspects of parenting, and friction can arise very easily. We have a lot to learn from each other, however, the messages get lost in the comparisons. One easy example to call out would be Pamela Druckerman's book "Bringing Up Bebe", where the examples of French parenting are painted as perfection and American parents are universally vilified in order to boost her own argument. Tarring all parents with the same brush doesn't help in the least, and obfuscates the suggestions which might actually be helpful because we have taken such umbrage at the assumptions and tone the author uses in describing her prospective audience. The good points are lost because the presentation is so odious.
And this is what I think happens at moms groups or in those conversations: one parent wants to assert their opinion/idea/method, but instead of saying "have you considered" or "oh, you know, we tried X and it worked really well...something to keep in mind" (and keeping the conversation open), I instead hear absolute statements about everything from potty training to red-shirting, and many derisive statements to boot. This is where it's easy to get our hackles up. I think many of us have friends who parent similarly to us in some ways and differently in others-- if we can abide by those differences by acknowledging them with support and empathy, we allow more space in the friendship (much like any other topic)... if we are concerned about always 'doing it the best way', we're going to fail anyway.
My step-mom has a great saying: "You can be *right*, or you can have friends." I really like that one; it forces us to choose our ultimate priority and to act on it. I have friends who parent differently than I do, but all of our kids are happy and healthy-- and still young, too. The proof is in the pudding, but our 'little puddins' have about 15 more years to cook! Too soon to know!