The last post makes very little sense. The subtle shade from poster howtheheck suggests Glendower Prep girls are not relaxed and are affected compared to Falkner House girls? That is actually quite a horrible thing to imply about a group of children under 11 years old.
Look, I have friends with girls at both schools and both are amazing institutions. Every member of staff I've met at each school has been committed, down to earth but extremely professional. I have visited both more than once and spoken to both headteachers and here is what I think:
Falkner is in a town house, so also has a 'cramped' feel. Unless you go for a school like Francis Holland or Kensington Prep, most schools in Central London schools will lack space.
Both these schools are highly selective. Glendower has a long established sibling policy (not sure whether Falkner also has one). I think any school that has a sibling policy but still yields such great results should not be dismissed so out of hand.
My friends with daughters at both schools say the pastoral care at their respective schools is very good. Both heads are inspiring individuals who are generous with their time for current and prospective parents. However, they are two very different personalities. I know a few families who have visited FH but would not send their daughter there because current parents have a rep for being snotty, and seem desperate in their attempts to curry favour with Mrs Griggs. It is implied (although I have never seen it first hand) that your daughter's path will be smoother if Mrs Griggs likes your family. I do get a sense that the girls at Falkner are being educated in a rarefied bubble. On the other hand, I know people who genuinely appreciate how much Mrs Griggs cares for her girls and their family. Mrs Griggs is very present in all aspects of her school's running. If she is your cup of tea then choose this school; it is fab. Especially if you have a son - they are opening a boys school in September. This will be run by one of Mrs Griggs' daughters.
Mrs Knollys is liked by all the families I know who send their girls to Glendower. She is relatively new and so some of my friends' girls have been there since before she assumed the role. They all say the school is now very much better as a result of her leadership. She strikes me as person who knows her mind but is willing to listen to the opinions of both parents and pupils. The work within the community and efforts to encourage pupil's philanthropic spirit is impressive. I was impressed by the music department and how music (theory) is taught. The ICT and art departments were very good, not least because of the inspiring teachers. Glendower does well in sports against other schools, and their science lab is fantastic. It is very difficult to get into because of the sibling policy and historically they lean towards offering places to local girls.
Girls from both schools are confident, charming and genuinely lovely young people. You could do much worse than sending your daughter to either of these schools.
My advice, after speaking to my friends with daughters there, is go with your gut. Or flip a coin.