Not sure if you’ll see this, but curious why you chose to apply through St. Andrews v. William & Mary? We are about to start organzing our app materials, and I note that the essay for the JDP on St. Andrews side is WAY shorter (400 words) than on the W&M side (up to 2000 words). Are there other advantages/disadvantages I’m missing?
The biggest difference is the school you apply to is the school you start at. (You can only apply to one or the other for the joint degree program). St Andrews also has a required interview, and I imagine is a much harder admit if you are a student coming from the US. Most of the UK colleges also require you to submit testing and may have minimum scores on things such as SAT and AP tests (UK colleges are less holistic in their approach to admissions).
Unless you are from Virginia, William and Mary is going to be much harder to get into than St. Andrews (assuming you’ve taken AP courses and have good AP test scores)