For an MSc - definitely Bristol.
Regarding a BSc - I would probably choose Durham, because of the "prestige" factor, as you said, but for postgraduate study I'd go for Bristol.
Durham's advantages are societies, firms and IBs campus recruiting to a larger extent, but they are mostly targeted at undergards. Bristol's advantages on the other hand is having a stronger econ department and foremost ranking higher in all postraduate rankings, where research matters the most (ideas repec; econphd etc.).