Sheffield is 10th best, Bath 14th best, for Chemical Engineering, according to Edurank.
Research quality for it is 88% at Sheffield, 83% at Bath, according to TCUG.
As is often the case with Bath, average entry grades for it are higher at Bath (80%) than Sheffield (66%). So the average student at Bath might end up being more successful partly because they were on average more successful to start with in their academic ability. It's a shame that this isn't reflected to quite the same extent in the ranking of the university's subjects themselves but Bath has become trendy with a particular set (including the sporty and 29.2% went to private school, according to The Tab) and being in an ancient city will help to attract students to some extent.