A couple of points here. I generally think that the supervisor is more important than the university so don't get too hung up on the prestige of that uni. I know of one former polytechnic in my field which has some of the biggest names in the field working in a large research group together. In the same field I know a prestigious university with one, middling potential supervisor.
Secondly, doing a PhD is blooming expensive, so ignoring a funded opportunity to work with an energetic, well known supervisor for an unfunded one at a prestigious university seems a bad choice, to me anyway.