I'm from Bristol but currently go to Bath Uni.
I would say there's more to do in Bristol (however that's more likely due to it being the bigger city), and it has a better night life, though if you don't drink or like clubbing then that's pretty irrelevant.
Architecture wise, Bath is prettier.
Bath is a campus uni whilst Bristol is not. Before applying, I definitely preferred the idea of a campus university so that may be another factor for you to consider.
I would say Bristol has a more global prestige over Bath, but once again that's probably due to Bath being under 50 years old whilst Bristol is over 100. However, looking at UK rankings, Bath is definitely seems to be "better".