Hi! I currently study at Leeds and I'm happy to answer any questions you might have.
From what I know, Bristol is more prestigious than Leeds, so if this is what you want it makes ore sense to go to Bristol. Its Biosciences department ranks higher in the league tables I've checked. I don't know what our Biochemistry course is like, so I can't vouch for it.
To be able to study abroad, you'd have to get a 65% in your first year, so if that tips the decision you'd have to make sure you can get that.
There's a lot of focus on career networking events and employability opportunities, so you could catch up through being able to sell yourself as a candidate, but I don't know our employability stats for specific careers.
I can't comment on the living costs. I do think our student union is better, it's one of the best in the country. Some people really end up involved in their student union, and some don't, it depends what's important to you. Your students union will give you societies to get involved with, extra support on things like employability and housing, and put on events.
Overall, choose based on what's important to you, and look at whether Leeds or Bristol better fulfils that list.
Both Leeds and Bristol have some great aspects.
Good luck at Leeds! I currently do Biology in a Joint Honours degree, I can't say I'd recommend my course here.