I couldn't pretend to know what's right for your kids, ER...but I had the experience of refusing a move, as a child, and here's what I think:
I agree that giving in if you really feel strongly they would do better with the move is not a good idea. You are their parent, and your instincts and research need to count.
I also think their feelings are natural, and must feel hugely important to them. Friendship groups at this age seem like your whole world.
I suppose, in your shoes, I would say both those things to them. I would validate their feelings, and talk about what scares or upsets them about going to a different school than their best friend/s. About how they could keep the friendships going, about how life goes on after school and that new friends and separations will happen to them all their lives. Treat them like adults in that sense, talk to them about growing up, but with lots of compassion for their losses.
And at the same time remember they are kids, and that your opinions count as much as theirs - holding on to your opinion is going to help them in many ways, in the long run.
Ooooh I wish you luck! I was supposed to move into the year above mine at secondary (in Y7) and the thought totally freaked me out at the time. I cried and was scared and bereft, and my parents thought they were helping me emotionally by leaving me with my friends and not moving me. Forcing me to move without acknowledging the fears and loss would have been worse - but in an ideal world, helping me to process my feelings and giving me a genuine choice (rather than a panicked resistance) would have been fantastic.