Whereas we would probably all like our DDs to have the natural born leadership and winning qualities your DD has, Macdoodle, it can be a flippin annoying trait in a child. We all know the one who has to win and it is not pleasant at times. I think you need to back off their friendship a little.
Think of your BF.. her poor little DD is forever trying to compete with your DD who is, from what you say, brighter, quicker, more clever, more of a leader blah blah... Yes, of course, we all like to be proud of our kids, but sometimes you can go one step too far - there is a fine line between a natural achiever and a smart arse (sorry!)
FWIW if my DD had complained that her friend had got a fringe the same as her I would have said 'Don't be ridiculous, it will grow out soon anyway!' It is sooooo unimportant and your feelings about it might possibly be rubbing off on your DD.
In life we all need dominant and passive people, leaders and followers, introverts and extroverts etc... but I think you are building your DD and her wonderful traits up far too much.
I have to say you have taken any minor criticism on here very well. Good luck!