I agree it's really difficult and it's not possible to avoid talking about it at all. However, I think the key is to never be the instigator of the conversation. Yes, answer if asked and if it feels right to ask about their choices in return do so, but just make positive noises or bland comments in response.
In the period before you know where they'll be going, you can say that you'll be applying to several schools (name them if needed) and will just have to wait to see where you get offers. If pushed you can name a favourite and try to make any reasons be just about that school, not that school in comparison to any other 'we liked the feel of it when we looked round'.
After everyone knows where they are going, again don't be the instigator of the discussions, nor get into gossip about who is going where. Just be honest about where your child is going and give a positive reasons which isn't comparative. Don't run down the local schools and if you need to say something, repeat a positive you've heard about one of the locals. Comments about how all the children yore discussing have such supportive parents etc etc help too. Say little. Once there, don't say too much about lots of sporting opportunities, any subjects not offered in most schools, small classes, great results etc etc. Stick to X making friends, teachers seeming nice and other things which aren't too controversial or don't set the school apart from others too much.
Basically, no-one likes hearing that others are receiving something different or better than themselves.....so simply don't say very much that sounds like it. If it helps people to think you're paying entirely unnecessarily, then that's fine - don't try to explain why you're paying or what you think you're getting for your money.
And keep up old friendships. They were your friends before and can be now. And it will be true that some of those children in state schools will be more successful and do better at school than yours, and having a wide range of friends and especially old and local friends is so important and school makes up only a small part of life.