When I was at Swansea University doing Civil Engineering (graduated this summer) most of the collaborative work that the engineering academics seemed to do were with Imperial College, Cambridge, Bath, Bristol and Southampton. None of them ever mentioned doing any work with Manchester.
Perhaps Bath is more involved in cutting edge civil engineering research. However Bath's undergraduate program may not necessarily be taught better.
Both are world class universities. If possible try to visit the universities before making a decision. As someone has already mentioned, they are very different cities. For an undergraduate I really don't think it makes much of a difference.