Di - I have to say, I've never looked around LEH as I have boys. I do have a DS at LU in the Midfle School years. He was offered a place at Hampton too, so similar choice some years ago. I would say the main factors for consideration are -
- do you want your DD to be travelling by coach to and from school for the next 5-7 years. Yes it's safe, but can also be a bit stifling or problematic if you don't like someone on the coach. Hampton boys will be on the LEH coaches too.
LEH is not really near any cafes where pupils can easily hang out after school (especially if they have to get in the coaches). At LU there is a lot of "hanging out" because the have Hsmmersmith and Chiswick in their doorstep. Nearly all travel to and from school independently in tubes / buses. They are a more streetwise, "Londoncentric" bunch as a result.
There are all types at LU, but in general they are all quite confident types. This could be a but overwhelming for a quieter child. I know of two super bright but more "bookish" girls from my DS' prep who were interviewed for LU, but then not offered places, which was a surprise tbh. They both went to LEH and love it.
LEH has slightly higher numbers if A star grades, but tbh the academic differences between these schools are pretty meaningless. They are all more than capable of getting the best out of your child academically. For instance, there are 10 maths sets at LU, but they are pretty much all expected to get at least an A grade. DS knows various girls who turned down places at SPGS because they wanted co-ed and now they are happily average at LU.
LU has a quite urban, fast paced atmosphere. It can be a bit of a "cool school". 
LU does not feel academically pressured in years 7 and 8. It seems to step up a bit after this though, but it's still fine. Homework is very manageable and not given out for the sake of it. The curriculum is dynamic and absolutely fantastic. It is an incredibly forward-looking school and always looking to innovate.
I think LEH may be a bit more nurturing possibly?
Anyway, those would be my thoughts. Good luck!