Both are certainly excellent universities. However, I would go for Durham's collegiate structure as you do have far greater support during your studies. Particularly at Cuth's. You always have an understanding ear. With people fighting your corner on not just your department, but also college, you should feel supported and valued.
Durham is aching with heritage, England's third oldest university, you are studying in a conservation area with a World Heritage Site on your doorstep.
Despite its vibrant student theatre and sport, Durham's nightlife cannot compete with Bristol's. However, this shouldn't be a problem. If anything it's a benefit. You have a small and (relatively) quiet city to study in. However, 12 minutes north by train there's possibly the party capital of the country, certainly the north with more theatres and museums alongisde its obvious pubs, bars and clubs. It surpasses Bristol in my humble opinion.
Away from Durham you have wonderful countryside, from the moors, market towns and castles of Northumberlad, to the entire coastline of the NE and also the Durham Dales. If that's your thing.
I can't speak for the departments however, I'll leave that to someone else.