We had a similar decision to make 4 years ago for our sensitive but internally quite confident DD. We chose LU and I think it probably was the best decision. They are both excellent schools so you can't really go wrong. We took an extra visit in the day time and that made us feel the atmosphere and confirm our decision.
Our DD was (and remains) certainly not cool and that has not been a problem at all. The year group is large 180 and that can mean you feel a bit invisible at first but the 'cool' gang (which is actually quite small) find each other, but so do the quieter, musical, arty, theatrical and sporty children. There is space for everyone to find their niche and the facilities are great.
We had a social blip in year 8 and once I informed the form tutor it was dealt with seriously and immediately. They take any bullying very seriously especially misuse of social media and pupils have to sign a contract. The PSHE programme is well thought through from social relations, sexual and drugs education to mental health and resilience work.
There is so much going on in terms of clubs, music, theatre and sport that it's quite hard to fit in school work. The school ethos is to get involved and the lower homework levels and fewer exams than other schools allow this without compromising public exam results.
As said up thread, the curriculum is innovative. The World Perspectives course is fascinating and assessed via soft skills such as presentations, a conference, PowerPoint, group work and research etc. so that the Latymer leaver has great skills for uni and work. This course replaces one GCSE and is UCAS accredited.
Unpredictably we needed support from the SEN department, known as Academic Mentoring. They are really fabulous and if your DD already has an identified difficulty I would guarantee that she will be well supported. I would really check out what G&L has to offer and compare.