I agree with you, Rolymo, that Whitgift's historical reputation is the thing that makes people chose it despite the fact that Trinity and Caterham are overtaking it academically.
Of course some people are also swayed by the lovely old building and flashy sports facilities (and the array of exotic beasties!). I'm not sure the headmaster is an asset, though.
You will also find a different ethnic mix at Whitgift to the other two schools (this is particularly noticeable at Caterham although becoming more obvious at Trinity now too).
Differences in opportunities - hmm, well T is definitely stronger in music and I think gets better sports results (I don't pay much attention to the latter). C has the benefit of being co-ed so drama may make mores sense there - although T import girls sometimes for drama stuff.
T is quite big on science/engineering - I'm thinking here of the Trinity School Racing thing - not sure if C do anything similar?
Re sports - football is pretty minor at T and rugby is big.
I think the differences are in the margins and you only need to consider them if your ds is really, really into one particular thing. For example, if he is a keen singer or musician I would definitely suggest T. Good luck!!