OP, not sure you'll get any information here that you won't get from listening to other parents at your daughter's prep school, especially if she's at the academic one. However.....
My impression is that Colfe's and BH have their work cut out in attracting the most academic senior school students, because parents who set most store by academic results and prestige (and let's not forget, have the money) opt for either the Dulwich schools (JAGS/Alleyns) or Central London or some of the prestigious Kent schools (eg Sevenoaks) and accept the commute of 1hr plus, or in the case of the Kent schools go for boarding if available.
The parents who set most store by academic results and want a selective school but don't have the money work towards the eleven plus. Because Kent and Bexley have lots of grammar schools, they are not insanely hard to get into, unlike eg Newstead Woods which is Bromley's only girl's grammar school and super selective. Plus they are handily clustered around the railway line and the A2/A20 so accessible - I am in Greenwich but have neighbours with daughters at Dartford Grammar, Townley Grammar and Mayfield.
Plus on the whole the Greenwich comprehensives have improved a lot over the last ten years.
So in practice, I think that Colfe's, BH, St Dunstans and Eltham College are all good schools but are competing hard for students. I agree Colfe's buildings are not gorgeous (IIRC the core ones were built when it was still within the state system) but it is a school with a good reputation locally. Anecdotally, I am told that they will work a lot harder to support individual students than some of the more "prestigious" schools. I don't know much about BH seniors - might ask my neighbour whose daughter is there.