Firstly, size doesn't mean quality, especially since it includes all the research fellows, that have nothing to do with undergraduate teaching. Secondly, the reasearch assessment, while the same, shows they both have top class research, but does not show which is better (there can be a huge difference in the top band, as one can be very good and the other absolutely exceptional), and more importantly has nothing to do with undergraduate teaching.
Then we get to the QAA teaching assesment. Now these are great for judging between universities which fall into the general useful range of the criteria. However when both have excellent ratings, there can be a huge difference that is not shown in the ratings. It's like A levels, one candidate with AAAB may be better than another with AAAA, as right at the top end, A levels are not good measurements of quality. Similarly with the QAA, while it's good for most, choosing between two of the top departments isn't a good use of it. Furthermore, the QAA themselves state that the ratings are not to be used totalled up, but are a rating out of 4 for each criteria, and thus does not reflect excelling in a particular criteria. All a top mark says is that it is very good at each of the criteria.
Oxford physics *is* demanding. Comparing either of the two universities to the vast majority of universities will show they're both hideously more work. However that doesn't stop there being a vast difference in the workload between the two.
So no, you assertion cannot be proved by "facts", the evidence provided shows they are both very good courses, which no-one I'm aware of is doubting. However it doesn't show they are equal by any stretch. As for the idea of Cambridge being better at sciences being said by "very ill-informed laymen", I think as a student at Oxford, who's seen, met and chatted to tutors and students from multiple colleges at each, I wouldn't be classed as an ill-informed layman. I have seen the difference in workload, the way employers, especially universities looking at grad placements, think of the two, and seen some of the exam papers they are set to take, and in my opinion, they are very much not equal. Yes, Oxford sciences are great, but Cambridge's are quite exceptional.
I agree, which place you like better, which course seems more appropriate, etc. is the most important criteria to decide which to apply to, but I disagree strongly that both are equally difficult, both to get onto and while there, and that both have an equal reputation. I love Oxford, I'm very glad I'm here, but if I was thinking of applying for a science, I'd have applied straight to Cambridge.