Hello- they are both pretty good universities I think. York has a really excellent reputation for political philosophy, so if you were thinking of doing a PhD in political philosophy then York might be better,(though it does have people obviously working in different areas as well) but thats just reputations I suppose. Durham is also good though, but I think it has more people working on things like security and IR (like David Kerr) than York. Its hard to say what impact the reputations of universities have on a PhD application- but I think most universities would maintain that PhD candidates are accepted on the basis of their academic record, proposal and 'fit' with the interests of potential supervisors. Sorry that this has probably not been a great deal of help, but I think its ultimately quite hard to say how important reputation is..