Hi Silver1, well done to your DD - they are both great schools.
We had a similar decision to make a few years ago and, as we are based in Chiswick, it could have gone either way. We liked both schools: NHEHS is down to earth, has a pool, is more ethnically mixed, is slightly smaller, strong in science; G&L has on site sports facilities, all girls are new in Year 7, offers IB and A levels, is very nurturing, the journey to school is much quicker and more local girls were going there.
For us, the clinchers were travel time to school (with G&L taking about 20 mins door-to-door whereas NHEHS takes 30-40 mins) and being able to make lots of local friends. HTH and good luck.