Westminster vs Haberdashers' Boys' School

Your best bet for Oxbridge will be Westminster. There’s no private school that rivals their acceptance offers.
As far as education received, you’ll do well at both if you put in the effort but Westminster has a large edge for admissions to Oxbridge.
Westminsters debate team is internationally quite well known
STEM wise, there’s better options such as Tonbridge or St Paul’s but their results are still insanely good
Music, if you’re a singer there’s an opportunity to sing in the choir at Westminster Abbey.
Sports you’ll probably be better at Habs. Rowing and cricket is very good at Westminster and they offer interesting sports such as shooting if that interests you. Sports such as football isn’t great and they don’t offer rugby.

Hi, I agree with most things you have written, but I fail to see how Westminsters debate team is good. They only start debating at year 11, meaning 2 years of missed comps if you transferred as a student there in year 9. Plus, as far as I am aware, only a few teams have actually performed decently. The HABS debate teams are far superior imo.