As an Oxford student who knows a lot of Tabs, it seems with every month I discover another fact which suggests that, academically, the filth are just on another level. Going through it on a (major) subject by subjct basis:
Maths: Tabs way ahead, the most respected undergrad course in the world. Have a special exam to justify it!
Sciences: Tabs have a notoriously difficult course with six days of lectures a week, and loads of depth. Again, more respected than Oxford and again I'd argue the most respected in the world.
Engineering: I'm not to sure about this. I've heard the Tab course is more respected but don't really know.
Medicine: Not on such sure ground but from what I've heard at Oxford, our medics think the Tabs work harder.
So in the sciences the Tabs are way ahead, everyone knows that. But I can't see much justification for Oxford's supposed advantage in the arts:
Economics: Oxford teaches this with hardly any of the mathematical riguor needed for research and which the Tabs have.
Politics: Oxford is ahead here, at least in terms of prestige. No idea about the rigour of PPE/MHP vs SPS.
Philosophy: I'd guess Cambridge is ahead here too as Oxford doesn't teach this as a single school.
English: No idea.
History: At Oxford history is rightly known as a complete doss of a course, whereas my friend at Cambridge is working her butt off because they just have much more work than us.
Law: No idea, though the Oxford course is tough.
Classics: This is the last properly tough course at Oxford so far as I'm concerned, and Oxford does hold a genuine advantage here so far as I know.
Geography: Don't know personally, but the only person I know who studied Geography said the Cambridge course was much better.
Languages: Don't know. Oxford course has a year out for no useful reason though, not great!
So in toto Cambridge seems significantly more academically rigurous than Oxford. But perhaps as a result of this, it falls short in other areas. The extra-curricular scene at Oxford seems considerably more vibrant. The student newspapers and the Union are much more successful in Oxford. My experience has seen far more Oxford students wandering about the City, and this is reflected in the Graduate of the Year awards, which have seen four out of 14 Oxford finalists (including a winner and two runners up) in the last year and no Tabs. If you're not going to be an academic, which most of us aren't...it seems it's still Dark Blues by 5 lengths...