I don't know a great deal about the Durham course, but I know a lot about the York course (as I'm doing it), so I'll try to help.
I didn't apply to Durham, partly because Durham has a reputation for being particularly disorganised - something which matters a lot when you are studying a course that involves 3 different departments. In fact, I heard rumours back when I was applying that they nearly scrapped the degree in 2009. York on the other hand is very organised - it has a centralised School of PEP that organises the degree, and it's done very well.
The York course is excellent. It has been around since the 80s, and has built up quite a reputation and an alumni network in that time. As far as I know, Durham's course is relatively young compared.
If you'd like more advice, PM me.
I would, however, suggest that you look at the way the courses are structured, and have a think about which city you'd prefer to live in. These will be much more important than any perceived differences in prestige - I don't think there is a difference, anyway.