What year is he in now?
We looked at both for DD but she ended up elsewhere as A levels weren't for her.
A level maths is hard. At either of PS or BP he will need a 7 or higher for his GCSE. (It should be less of a step up with the new GCSE spec though.) I wouldn't do it with a just scrape a 7, more like expecting an 8 but might drop down, or at minimum solid 7 iyswim?
PS has the better reputation, but BP seems to be coming up a storm as far as I can see. Our impression was that PS was a step further away from school, pastorally BP seemed a bit better and generally friendlier. PS has the better reputation for science subjects I feel. The hardness of the A levels will be the same either way.
Ask about drop out rates, and how they judge who is allowed to continue to second year. Under the old system of AS exams places could weed out lower achievers to make their headline results look good. Don't know what will happen now ASs are going.
Friends DC complain about overcrowding at PS - no where to go at lunch time, hard to find space to work during the day, busy busses.
Which is easier to get to from you? If they don't have to be in all day it could be useful to be able to just go in for the lessons and go in late / hope early. If you post on the main Secondary Education board you may get a number of responses as there are quite a few Hampshire parents posting there.
hth