Hello there, an interesting question, and one answered by my daughter's own experience a few years back.
Firstly, I think St Andrews history are more stringent on what grades are required, that is if she hasn't got the grades already. Bristol might be more lenient depending on the type of school she attends. Something that riled dd was the fact that Scottish AND EU students did not have to pay tuition, whilst she from 200 miles away did. That's a consideration.
In regard to league tables, in hindsight I would not put much on them. Especially when it comes to employment; higher league table position doesn't necessarily translate as better employment prospects. One ought to remember that St Andrews is rather difficult to reach and so if your dd had her eye on a job in the city of London, it would be a pain to get down for interviews. In my opinion, Bristol is just as good as St Andrew's for employment prospects.
I don't think a Scottish MA is really seen as the same as a postgraduate MA. It is much the same to the Oxbridge MA. I was once told that the reason the courses in Scotland are four years is to allow for the Scottish students to catch up, as their secondary education isn't to the same level as A level/IB. How true this is, I don't know; nor do I want to get into the politics of such things.
Next, St Andrews history course is brilliantly flexible , and the system there allows people to mix and match to their interests. However, this does allow for a different degree in the end if say you decide to specialise in mediaeval history and economics. They have a particularly strong mediaeval history department, and on the open day we were very very very impressed by the academics there. The buildings are stunningly quaint.
Bristol buildings in her opinion weren't quite up to scratch in the historic side of things! Of course they do have the oldish buildings too. The history faculty building lecture theatres were quite odd from what she said. Although the staff were friendly, it seemed far more progressive/leftie. The course too was very focused on modern history and in general themes such as colonialism etc which is very fashionable at the moment, but if that is where your daughter's interests lie- brilliant!
St Andrews History seemed more traditional.
People make a university. The ones dd met at St Andrews actually put her off the place as they came across as quite snobbish, but others were very friendly! It seems quite small and close knit. It does have lovely traditions such as gowns too.
Bristol students in general are far more extroverted/big city than those at St Andrews. Bristol has a large clubbing scene. The people dd met were cooler or more urban. She sensed that they were slightly. more mature too. Most 2nd years onwards live in Clifton which is a gorgeous safe area, with lovely large Georgian houses.
In terms of cost, both are expensive. No good university will be cheap. We did hear horror stories of renting in St Andrews, such as 10 hour queues etc.
In the end however, dd took a gap year as she couldn't decide, and now goes somewhere else completely! In hindsight, she says that from visiting friends at Bristol, she'd have gone there as it's much more her and she'd have probably swapped courses. For her, the St Andrews degree was perfect and still a much better fit for her than where and what she currently studies elsewhere but she couldn't see herself sticking four years there. I think she needed a bit of small city after living in the country all her life. Several of her friends are now at St Andrews and several at Bristol, all enjoying!
Tl;DR: If she is more a city person and is sure she loves the course there, go for Bristol, she can't go wrong and will come out with very good grad prospects.
If she is a more small town person, and is not so sure about the Bristol course and has interests outside of modern history, got to St Andrews.
Please ask me any questions at all, willing to ask dd!