as I've been at one and I am currently studying at the other I will throw my two pence in :-)
I suppose answering the question of which one is the best is determined by how you measure the two universities against each other and there are many ways of doing this. I would think it is better to compare the two in specific feilds and courses rather than trying to give each university a blanket rating and using that as the basis for applying. There are a few league tables both national and international which try to do this but I would always take league tables with a grain of salt. no one doubts that Cambridge and Oxford are both world class universities but consider the differences between the rankings that both univerisities get in different league tables. The point being: there is no absolute way of measuring the two against one another. I think a lot of the time choosing one over the other can come down to personal preference.
I often hear things like: Cambridge is better in the sciences and Oxford in the arts. Although I tend to think that such sentiments are unfounded and rubbish.
Also consider that there are plenty of other univerisities in the UK which may be a as good if not better in what ever field you wish to do your PhD in.