Thirty years ago I went to Croydon High and my brother went to Whtigift. I was aware of the fee difference and felt resentful. Not of my parents, but of Whitgift, because it had a huge amount of money and kept it all for boys - just Trinity and Whitgift in the foundation then.
With the benefit of hindsight, i'd make three points.
First, more expensive doesn't mean better. CHS set me up well for life - decent grades, but more importantly confidence in myself and a sense that the world was a good place. In contrast, Whitgift failed my bro - didn't seem to care that a bright boy became disengaged and badly behaved. I'm sure things are different now, but I sense that Whitgift spends lots on frippery... e.g. peacocks, big scholarships to children from wealthy families.
Second, CHS has good sports facilities. However, with hindsight, Whitgift seemed to have more teams - rugby teams A-D. At CHS I didn't make the cut for the netball squad aged 11- I think there were only two teams, and the squad got games and training so they got better and better and no-one else had a hope of improving enough to join. For those of us that didn't make the cut it would have been great if they'd tried to help us find a sport we were good at, but PE was largely sports where i'd failed to make the squad. I think girls schools need to work hard to help girls find exercise they enjoy.
Finally, the solution is simple. Use the money saved on your daughters' education for extracurricular activities. Take her sailing, skiing, visit Japan to find some pokemon, give her a £4k violin or even a pet peacock.