Hello,
I will offer yet more anecdotes. Dartmouth has been mentioned several times in this discussion. I worked at Dartmouth before joining St Andrews, and I would say that the two are directly comparable. In some areas St Andrews is much better, e.g., contact time. And in other areas Dartmouth is much better, e.g., facilities; it's hard to compete with a university with its own skiway, although the town of St Andrews does have seven golf courses! But in most areas, e.g., breadth and quality of courses, opportunities for students, employment rates, or the quality of students, I would say that the two are more or less the same.
Whether this comparable quality translates to comparable "prestige" is something that I am unable to assess. But if you can somehow equate "prestige" and "reputation", then I will provide more anecdotes. My degrees are from Cambridge and UCL. When I worked in the US and discussed my academic background, most people had heard of Cambridge, although some asked if I actually meant Harvard or MIT. Practically no-one had heard of UCL, and most people thought that I meant UCLA. This was rather surprising to me at first, since UCL is quite well-known in the UK. Similarly, when I was returning to the UK, I applied to what many British students would perceive to be well-known institutions within and outwith the Russell Group and so forth. When it came to making a choice from my offers, St Andrews was by far the most well-known institution amongst my US colleagues.
Has your son visited St Andrews yet? While I would say that it is comparable to Dartmouth and many of the other institutions mentioned in this thread, he will have a very different experience at St Andrews versus, say, Chicago. A visit may well help to clarify his thinking.
Tristan Henderson (in a personal capacity rather than as a St Andrews Admissions Tutor)