I believe that a bright child can do well in any good school, but Britain being the Elitist society that it is, having attended a good grammar or independent will look good on any resume and welcome the child into "the club" and set him/her apart.
My son gained a place at an independent. He was a bright child doing very well at his nurturing and outstanding primary.
He is stressed with the pressure at the independent, and he is frustrated by not being in the top set anymore. OPs daughter has a valid concern here.
I honestly think that a school that can turn out a good education for a myriad of children of different ability levels is BETTER at education than a school were all the children start very high up the ladder. Ops ex seem to recognize this.
My son did not know anybody when he started s 7. He was looking forward to starting s 7 and making new friends, and he is not looking forward to starting s 8 now. I asked him why the difference and he said "I did not know last year that most of the other children are superior arseholes"
So, now I am not looking forward to s 8 either. Ops daughter is right to be concerned about friendships and fitting in. However, friendships should not be dictating where a child is educated.
If you are of the belief that there is more to a childs development than a (at least on paper) good education, you may chose to go for the school where the child may shine and build up their confidence, rather than building it down.
That is just my take. (And yes, we are anticipating a change in schools for our son before Christmas, and I will be to a outstanding state secondary we have been in touch with)