11mum89 - on LU v G&L, I have / have had DC at both. This is only a personal perspective, but for what it's worth -
LU is a more dynamic school, yes.
On the other hand, G&L has a much calmer and 'kinder' atmosphere. Less 'behaviour' (inc bullying) goes under the radar and staff seem more intuitive / orientated to the pastoral care side of things. It's a very pro- female environment and, on the whole, girls are confident without being aggressive, focused, mature and supportive of each other.
At LU, my feeling was that they tended to let certain problematic 'personalities' run loose and the social atmosphere was much more fractious and insecure (under the surface). Staff were more focused on all the activities etc etc, rather than day-to-day well-being. The school is more hectic and there is less hand-holding or personal connections between teachers and pupils in the early years.
LU better for trips (activities week, etc).
At G&L they seem to do some physical activity daily as standard (not so at LU).
Teaching is generally excellent in both schools. Homework levels are very similar.
Drama and music more inclusive at G&L.
This could change by the time your DD hits sixth-form, but at LU they do three A-levels, plus EPQ (recommended), alongside what they call a 'carousel' of other term- long courses which lead to a Latymer Diploma at the end. At G&L, they do either the IB, or it's 4 A-levels, plus EPQ (I think?), with the option to drop an A-level at the end of Year 12 if it's too much.
Those are the main differences. LU is more socially-diverse (I think 25% are on some form of bursary compared to only 10% at G&L). If I had to say which is a 'happier' school (based on what I know from DC friends and talking to parents over the years), I would say G&L because on the whole, girls seem more settled and secure. But this is only my personal perspective, of course.