I don't know much about Chesham or AGS specifically, other than that they are both good schools.
However what I would say is that personally I would always opt for a mixed school over a single sex one for my child. I went to an all boys Grammar school myself and while I did well academically, I've always felt it held back my personal and social development as a teenager. When I went away to University I was quite shy and awkward around girls unlike my friends who'd been to mixed schools who were far more confident and relaxed.
Back in Victorian times men went out to work, women stayed home, men socialised with men and women with women. Other than the unpleasant interaction necessary for the continuation of the species, there was very little interaction between the two
! Thankfully these days its different and out in the real world men and women work, study and socialize together. So it seems a bit bizzarre to me that in this country we still have single sex schools which effectively cut kids off from members of the opposite sex during some of their most important years of growing up and forming social relationships.
Saying all that though, that's just my own personal experience and opinion. Everyone's different and the most important fact is where you child thinks they will be happiest.
(BTW in case anyone's worried I did finally get over my shyness and and have a wife and child to prove it!