That's quite a shopping list.

Final year students at Sheffield rate the quality of teaching and learning higher that those at Bath. See the following from the National Student Survey, as published by
The Uni Guide.
Bath (
source):

Sheffield (
source):

I'm not sure from where I'd source this information. I'm not aware of either university being in particular financial difficulty.
The Complete University Guide rates Bath 3.30 (83%) for "research quality" and Sheffield 3.53 (88%). I know this isn't really the metric you wanted, as this is a measure of the quality of the research undertaken in the university (for Chemical Engineering), rather than being an indication of how much they lead students into research. (
source)
I'd say that both unis have good industrial connections.
Bath is a safer city. According to the Avon and Somerset Constabulary, there were 327 crimes reported in Bath city centre in February 2025 (
source). According to South Yorkshire Police there were 674 in Sheffield (
source) during that same month. These numbers will be impacted to some extend by the size if the city centres (Sheffield's is larger), but not to a significant extent. Note that I haven't made any allowance for where either uni is, as you referred to the city being safe, not the uni or the area around the uni.
According to
Uni Compare, Sheffield ranks better for student life ("Students rank their universities based on how good the social side of uni is"). Sheffield ranks 11th with a score of 3.96, whilst Bath ranks 69th with a score of 3.65.
They both reasonably-sized cities, so you're going to get a wide variety of restaurants in both.
It's more expensive to live in Bath than in Sheffield. According to
Save the Student, students at Bath spend an average of £445 per month (excluding rent) on living costs, whilst students at Sheffield spend an average of £422. You can get an idea of likely rentals costs
here for Bath ("One bedroom flats in the city centre can be found for around £1,100 per month, or you might decide to rent a room in a shared house for around £810 a month per person") and
here for Sheffield ("If you prefer to live alone, a studio apartment in the city centre will cost around £830 per month, and if you’d rather share a house with friends, a three-bedroom apartment will set you back around £1,450 on average."). So, it's more expensive to rent in Bath.
The main things?!

Now you need to weight each of those criteria to see which of the two "wins".