They are both good schools, so you are very lucky
We looked at both for our son recently (didn't get a place at HH and we didn't chose EH either), I would choose HH because:
1) it's coed. You know your daughter best and you will have a better feel if that's important for her or her sister
For us, this was the major reason why we didn't chose EH.
2) HH is more diverse. Again, you will know best how important this is for you.
3) At EH, there is some sort of assessment at 7/8 in order to go into the upper school (that's for the boys school, not sure if for girls too). Which means that if your child is bottom of the class (unlikely, I agree) you will need to find another school at that age.
Sounds like you have to decide between a school that you possibly like more vs a school that's closer, so more convenient. I'd say lots of people in nappy valley have a very similar decision to make (and some chose convenience while others choose the school they like best). You'll have a gut feel of what's right for you, and that's probably the right decision.
Best of luck!