uni reputation

Its marginal - and since you can't 'measure' something as nebulous as 'reputation' its pretty meaningless anyway.

Chemistry applicants are in short supply and many Chem courses at leading/RG Unis regularly go into Clearing - its to do with a shortage of Chem teachers in schools, and the majority of A level Chemists applying for other Uni courses and not straight Chem. This leads to a shortage of Chem grads - and means that no-one is going to care much where you got your degree - just that you have one. Both are excellent Universities, and neither would give you more graduate opportunities than the other.

Look at the courses in detail - which optional units would you choose - for all three//four years of the degree. Which course will you enjoy doing - one more than the other? Are there any extras like industrial placements or study abroad etc? Look at what research each Dept is doing, and the research interests of staff within the Dept, and the postgrad courses they offer - this has implications if you want to stay there for a Masters or PhD.

Look at the Campus Tour and Open day films on YouTube and think about where you would feel more comfortable.
And cost of living - Bath has high rents compared to Loughborough, and you wont get extra SF to cover this.

'Rankings' are def. not the way to chose a University - the results are inconsistent across tables, they measure things that have no impact on undergrad degrees - and they can't tell you if you will like the course or like being at that Uni.