I have had DC at Cambridge and St Andrews - I'd say the calibre of students and the quality of teaching is very similar. Weirdly, St Andrews doesn't seem to have as many Scottish as you might expect. Walking around you hear a LOT of Americans. I think it's maybe even 20-30% Americans there.
The best thing about St Andrews is that degree programmes are far more diverse and flexible with many more options for dual honours degrees. In fact, students don't actually have to decide on their actual degree title until the end of the second year. I think, at an open day, they said about 30% of students come out with a different degree to the one they went in for due to having experienced a subject in their first or second year that they hadn't had an opportunity to study at A-level - eg. you could very easily go in to study English Lit, take Law and Modern History as your compulsory other two modules in the first year, and come out with a Law degree. Or a History degree. It's much more like the US system where you only 'major' in the second half of the degree programme. I think a lot of people in England aren't aware that the Scottish degree structure is quite different in this respect (well, we had no idea, but might have just been us).
The other huge benefit of St Andrews is the overseas study option in the third year because students come out with another institution on their academic record - eg. UPenn, Berkeley etc. There are very strong exchange links with a number of top US universities, but also many other global institutions.
On the other hand, Cambridge is obviously a much larger uni and has the international reputation that still carries clout. You can't really fault the tutorial system for value for money. I know people say many organisations recruit blindly, and I'm sure this is true in some industries. But not in all! The name does still carry benefits - but like anything, it depends on what they do with it.
I think we are lucky to have amazing unis in the U.K., as such a small nation. The London unis - Imperial, LSE and UCL -are also fantastic in their own ways. You can't go wrong with any of them.
ST Andrews and LSE do appear much lower in the QS global - I think this must be because they are smaller institutions. I mean, in London, everyone knows that Imperial and LSE are equally competitive entry - it's just one is a STEM and one is a Social Science institution. Yet, Imperial comes top of the QS Global with MIT etc, whereas LSE is much lower. I'm not sure why.