The sciences/humanities dichotomy is, I'm pretty convinced, a complete myth. Both universities are very good at both, though each may have particular strengths in different subjects. Moreover, 'the humanities' (or indeed, the sciences) are not a hegemonic unity, and a student will not only have a very different experience from faculty to faculty, they will also have a very different experience within a single faculty depending upon their research interests. For example, I'm interested in intellectual history; for somewhat bizarre reasons, the really strong intellectual historians for my period are mostly in the English faculty at Oxford. At Cambridge the opposite is true - the English faculty is, I have heard, quite old-fashioned in its interests, whilst the History faculty has some very hard-hitting intellectual historians. At research level it's so individual that you can never say that one university is 'invariably' better than another -- if the person who specialises in your subject is there, then you'll probably want to go there, regardless of the perception that one is better at the humanities than the other.
This is also linked to the funding issue that Corinna mentioned. In an ideal world, funding would go to the objectively best candidates, but I think that especially in humanities it can certainly help
if your proposed research closely reflects the research interests of someone in the department you're applying to. I was never even remotely considered for funding at Oxford, whilst Cambridge gave me funding after being on the reserve list, and a couple of other universities considered me for funding. Though of course there may have been a different pool at Oxford, I'm sure that a contributing factor was the lack of synthesis between what I wanted to work on and the overall interests of the faculty here, whereas my selected supervisor at Cambridge wrote a book on a very similar topic.
Finally, the quality of the two towns as places to live is very subjective! I love Oxford very much but it has some downsides that Cambridge doesn't seem to have. For example, Cambridge feels a lot safer. Having lived out this year in Oxford I've come to really dread the muttering (or yelling) drunks on the bridge and in Cowley in the evening, whereas Cambridge at night just feels like a deserted village to me. Also Cambridge is in East Anglia, the dryest place in the UK, whilst Oxford has a micro-climate permanently set to 'soggy'.
Not to put off anyone who is coming to Oxford, as it is lovely! -- but I think the Oxford vs Cambridge decision is one that comes down to personal preference rather than any objective fact of one being better than the other, either academically or as a place to live.