As RichE has said, I'm not sure how you're making that assessment. In the first year, splitting into different areas:
1)
Introductory courses: Cambridge has a Numbers & Sets course which covers proofs, naive set theory and an introduction to elementary number theory. Oxford splits this into "Intro to uni maths" and "Constructive maths". This is an area I agree that Cambridge's treatment is more cohesive than Oxford's.
2)
Linear algebra: In the first year, Oxford's Linear Algebra I & II courses have a more "pure" course than Cambridge's Vectors & Matrices course.
From the Cambridge course, if you take out Complex numbers (2 lectures; covered in a separate Oxford course), Tensors (around 5 lectures, not covered by Oxford in the first year), and the quadratic forms / rotation matrices stuff (2 lectures, covered in Geometry instead). Oxford's course has a separate Geometry course which focuses on the use of vectors and matrices in geometry.
3)
Groups: Cambridge's course seems similar to Oxford's, once you take out the additional Mobius group stuff covered in Cambridge's course. I think it's fair to say this stuff is non-core at best.
4)
Analysis: Both Oxford and Cambridge cover single-variable calculus up to integration. The courses most differ in the number of lectures offered. Cambridge's 24 is extreme (i.e. it covers the material very quickly, more so than any other university I'm aware of).
In the second year, Oxford has a compulsory set of courses including:
- Linear algebra (I assume they're similar in style, however note that Oxford is happy to define a vector space over an arbitrary field whereas Cambridge defines over
R or
C only. Courses look to be similar in content otherwise.
- Rings (Oxford has a couple of lectures on this so everyone knows the definitions)
- Metric spaces (covering similar material to Cambridge's "Metric & Topological spaces" without the Topology bit, obviously)
- Complex analysis (note that everyone in Oxford is doing this with a "pure" approach; Cambridge allows you to choose between "Complex analysis" and "Complex methods", the latter being more applied in nature).
- Differential equations (Oxford's course includes Picard's theorem - existence of solutions - which is a more pure approach than Cambridge which covers DE's in methods courses)
The fact that Cambridge doesn't have any compulsory courses in the second year means that many people will not have done as much pure as they would've done at Oxford.
In addition, the differences in the optional pure courses in the second year are, briefly:
- Oxford's "Rings and Modules" and "Group Theory" courses are on a part with Cambridge's "Group's, Rings and Modules" course, except Oxford's Group Theory" covers free groups, composition series and the Jordan-Holder theorem, so seems more in-depth
- Oxford's "Integration" course provides an introduction to measure theory, which you don't do in Cambridge until the third year.
- Oxford's "Topology" course covers the topological spaces part of Cambridge's "Metric and Topological spaces" course, plus some introductory topology which isn't covered by Cambridge until the third year (e.g. simplicial complexes)
- Oxford's "Number theory", "Projective geometry", "Introduction to manifolds" and "Graph theory" covers pure material that is left to the third year in Cambridge.
The only material areas that I think Oxford doesn't cover are multivariate calculus (e.g. differentiation of functions between R^m to R^n) and Cambridge's "Geometry" course.
I think it's fair to say that Oxford's course covers pure more deeply than Cambridge's, at least for the first two years. Why make a random claim when both unis put up a wealth of information and you can just have a look for yourself?