Too be honest, isn't St Andrews just Scotland's answer to Oxbridge (not in a bad way though!). St Andrews is closer to Oxbridge than say, Edinbourgh. Despite that fact there isn't a huge differece in terms of the quality of the education between the two, even then it depends on the individual, some would flourish somewhere like Oxbridge or St Andrews, others might prefer somewhere like Edinbourgh or UCL.
I doubt there is THAT much academic difference between the two. The people who apply to Oxbridge, more often or not also apply to St Andrews, UCL, LSE, Imperial etc. So anyone in the top 5 or so universities tend to be interchangable to a certian extent. The only differance is whether or not they performed ever so slightly better on their A Levels or PS. Any even someone who wasn't from either university would be able to tell you that that is hardly a good judge of intelligence. Arguably Oxbridge have interviews and stuff to get around this, but they all say the prescribed thing...
The courses are really quite different, I know St Andrews is a lot more flexable, whereas Oxbridge is straight-foward and very structured. Which could be good or bad depending on what your looking for really.
Both have the steriotype of being middle class, privately educated rahs. Rightly or wrongly. But there really isn't as strong a steriotype in the universities which are a little bit lower on the league table (I'm talking 3rd, 4th, 5th... or any Russell Group uni actually).
But. I'm going to go out on a limb here and say (gasp!) that surely it doesn't matter if you go to the 1st 'best' university in Britain or the 3rd? More similarities than differences in terms of the collages, people etc.