The poster asked for a comparison between the academic rigor of St. Andrews and a US school. A discussion of Oxford is off topic and a discussion of cost is off topic (for the poster although I would hazard a guess not for the parental units).
My daughter has a H.S. friend (very good student who thought she would but did not get into a top 20 US school) who attends St. Andrews and apparently finds it rigorous and highly satisfying. I have heard generally very positive things “through the grapevine” about the academics and school spirit. UK schools don’t give a hoot about extracurricular activities, so a hypothetical UK school that is precisely as selective as a hypothetical US school would tend to have more academic students.
Rather than rely on this forum, it would be highly advisable to seek out Americans who went to a similar high school as yours and pump them for information. I think that means head to Scotland. If your parents won’t foot the bill, it probably means they won’t be comfortable with the unsubsidized tuition.
Lastly, while you didn’t ask about them, there are big differences between the US and UK systems that you should understand before making a decision.