Hey - I got into Cambridge this year, and come from the UK in a school that gears people up for admissions.
Cambridge and Oxford are soo different in terms of courses. You said you’re interested in business - the closest Cam has to this is Economic or Land Economy tbh. They have a Part II course called ‘Management Studies’ BUT you can’t apply to this for undergrad!!! You can only skip half way through your degree on to this. I’m not as familiar with Ox courses but I think Economics & Management is the closest you’ll get to business.
It’s useful to note Cambridge doesn’t do joints, but Oxford does.
If you applied to Cambridge you WOULD get an interview tbh. They interview something like 90% of apps, and given your stats are solid (which is generally how they filter out the first round of people), you should be good to go. Plus, it’s likely you would have to fly to Oxford and get interviewed in person there too - most Americans I’ve seen have to, and my friends met a lot of Americans at interview.
Oxbridge will ONLY care about your academic and interests in your subject. You literally could be a Michelin star chef and they probably wouldn’t care. Similarly, if you want to mention your ECs - link them to your subject. EG: I applied for languages, and I linked the fact I’m in an award winning film company to my interest in film as a way of exploring cultures and love of foreign film.