I can't say for certain, but I'm 95% sure the SATs will be more important. My reasons for thinking this is a) ALL students have to submit the SATs. It's a standard test that everyone must do. An American admissions team will understand and receive the SAT better than the GCSE. b) If you retook the SATs, then the SAT would be a better indication of your academic strength now as opposed to when you were 16.
The SATs are important for everyone, no matter if you're an international student or not. They're not going to base their decision on the UK equivalent - they will look at your SATs. Therefore I strongly strongly recommend you take the test again. You wouldn't really have to take the test until July, Sept, Nov depending on when you apply, so you have plenty of time to prepare. I prepared for my SATs in one month and passed with a reasonable score.
If you don't retake the SAT, they will use your Year Nine ones. You have to submit SATs - no way round it! Of course there are some other colleges other than Chapman that don't require SATs but most of them will. Are you planning on applying anywhere else in the US?
Most of the things they need will be listed on the Common Application. But you're going to have to do your research into what each college will want. American universities are rather strange - unlike the UK, they don't interview as many students because so many students apply. So, they require a lot more information when you apply. So an application usually consists of a General application and a Supplemental application. The General application is usually reserved for the "general" things like basic information, personal statement, recommendation, grades, and so on. It's the UCAS part of the application. The Supplemental application is more like the interview. It gets more into specifics about why you want to study the major you've chosen and tries to learn more about you as a person.
Take Dodge College as an example. As I mentioned, to apply to Chapman you have to apply through Common App online. Common App allows you to fill in the general application which will be sent to all universities you apply to. Then, each university will have a separate supplemental application listed on Common App. Each supplemental application will be different for each university. Dodge College's supplemental application asks for different things depending on your major. You can find the requirements on the website but I believe you have to have yet another letter of recommendation, a creative essay (with a prompt given), a creative resume and then an extra task depending on your chosen major.
Quick note on personal statement, bear in mind that American personal statements usually require different content as opposed to UK ones. The nice thing about most American PSs is that they give you a question to work with. So don't start writing your personal statement willy nilly until you know exactly what they want. Do your research and look on each college's website. They will list the requirements and tasks on the website. That's usually how you get your information!
Sorry if I've told you a bunch of stuff you already know. I just remember when I started applying to America I had to find out a lot of this stuff by myself, and it's lovely to help someone! I'll keep you posted and let you know if I got into Chapman. I've already received an acceptance letter from Loyola Marymount University as well.
P.S. I'm actually a girl, lol