DD chose Bristol over Bath for maths. Even though it was meant to be her insurance (Oxford and Imperial were here other choices)
Personally, I also had the feeling Bath might have the better reputation, but from what I saw, it only edges a few league tables and the gap is small and inconsistent.
What made the difference was fit. Bath felt more structured and a bit school-like, Bristol more like a traditional university with more independence. That suits Dd better. The offer holder day professor at Bristol was also very convincing. Whereas the taster lecture was terrible according to Dd but she says the whole course looks interesting.
Re outcomes, both do very well, I found. Bristol might have a slight edge for London-facing finance / IT careers just due to size and alumni. But in the end it comes down to what the student makes of the opportunity.
So for Dd it was hard to decide which uni is better so in the end she went with which suited her more. She‘s also used to city life and felt at ease in Bristol
Given your DS already likes Bristol and has his brother there, I can see why it appeals. What’s your take?