The Mathematics choice
Analysis and Approaches or Applications and Interpretation
The two IB Mathematics courses are treated differently by the two universities, and the difference depends on the course you apply for. It is better to settle the course shortlist first and then read each page's exact wording.
Oxford: usually either
Oxford's international qualifications page says that courses that state they require Mathematics accept both courses at Higher Level, apart from Chemistry, and that where Mathematics is only recommended either course is acceptable.
Oxford Chemistry: the exception
Chemistry accepts Higher Level Mathematics, with 766 at Higher Level, 7 in Chemistry and 6 in Mathematics. With Standard Level Mathematics it needs 776 at Higher Level, 7s in Chemistry and a second Higher Level science, and 7 in Standard Level Analysis and Approaches. Do not read this as a rejection of Applications and Interpretation at Higher Level: it is a rule about the Standard Level route.
Cambridge: asked for, expected or recommended
Cambridge uses three different verbs. For Computer Science, Engineering, Mathematics and Economics it asks for Analysis and Approaches. For Natural Sciences (Physical) applicants taking Higher Level Mathematics are expected to take it. For Natural Sciences (Biological) and Veterinary Medicine it is recommended for the most competitive application, though Applications and Interpretation will also be considered.
If your school does not offer Analysis and Approaches
For Computer Science Cambridge says to contact your shortlisted Colleges for advice. Do that early and keep the reply, since it is the College that will tell you whether you can apply.