As I understand it Tiffin offer, in the end, almost 300 places from 1800 applicants, which is in 1 in 6 chance of success (PAN is 140).
I'm not sure what Hampton's position is, but I would guess that it is similar in that half of offers probably don't get taken up.
I know they are more oversubscribed than the RGS, I believe more like 5 or 6 to 1 rather than 3 to 1, but obviously the further down the pecking order (if people are applying to four schools, say), and the more competition there is, the less meaningful that is - some schools would need that many applicants per place just to fill the places with no selection at all! I think it says in the GSG but I don't have mine to hand currently.
One of the thing with Tiffin is the selection procedure is more transparent and if you're shit-hot on IQ tests (effectively), than that's it, you get in, whereas these private schools can decide they do or don't like you for any reason under the sun - from the school's reference, to your choice of sports/extra-curricular activities, music, or anything, so no boy is ever a cert really with these highly sought after private schools, whereas it's quite possible to be a cert for Tiffin i think.