Choosing between PPE at Oxford and HSPS at Cambridge

So, I got a B for AS History, quite a low one, and dropped it this year. All the other subjects are fine, predicted A* for all the three of them (Politics, Maths, Economics), but my average UMS is still around 88%. I've always wanted to apply for PPE, but my school teachers say that as it is very competitive, my chances of even getting an interview are low no matter how amazing my personal statement is or how well I pass TSA. They advice applying for HSPS as its acceptance rates are much higher than those of PPE at Oxford. However, as far as I am aware, Cambridge requires to disclose UMS scores while Oxford doesn't, and this then puts me into disadvantage due to my low average. Moreover, doesn't the fact that a course is names Human SOCIAL and Political Studies imply that the admission tutors would place an emphasis on the grades an applicant has obtained for a Humanities subject? (My teacher rebuts this argument with the reference to the fact that history is a "useful preparation" subject for PPE at Oxford as stated on their website which may diminish my chances at Oxford, while on Cambridge website there is nothing about subjects recommended for HSPS and thus no reason to worry).
Generally, I am interested in international relations and politics, so being accepted to either of those courses would be great, but as I spent the whole last year dreaming about Oxford, I would prefer PPE if my chances of getting in were no less than for HSPS. If, however, I stand no chance of getting into Oxford, I would gladly apply to Cambridge as HSPS also seems fascinating. Regarding GCSE - I haven't done it because I am an international student, but I graduated from my country's high school with all the highest marks for all the subjects. Besides, I have done lots of reading/work experiences/volunteering and would be able to express my passion at the interview, so the main question is which university is more likely to invite me for it?
Thank you very much in advance