What's more important during the admissions process: AP exams or SAT Subject tests?

It depends on what school you are applying to. If you look at the Top 100, most of them have taken a moratorium on SAT Subject tests and Yale, MIT, and Caltech are Test Blind with regards to Subject Tests. So submitting Subject test scores isn't required but if you have great scores (720+) they can support your academic record in that subject or compensate for a lower grade. AP exams are less important than taking AP classes IMO. So if your school offers 20+ APS, and you've taken 8-12 of them, that shows course rigor and that you've challenged yourself. It's less important that you got 4s or 5s in them than getting A's in the class.

By now you can probably tell that T20 private colleges really don't want to reward you for AP exams and many of them including Williams, Brown, etc don't even give you 1 college credit even if you have (10) 5s. They want you to take their own classes and experience their program, not allow you to graduate 1 year earlier. State schools give you more college credit even for lower AP exam scores like 3s and 4s so if that is something you want to get, I would research AP credit on your college list. At some point, you will see that your Top schools are not that generous with APs, they just want you to have taken them because you challenged yourself and passed the threshold to be a viable applicant. If you have both great AP exam scores and Subject scores, by all means submit them. If you had to choose 1, I'd choose AP exams and taking more AP classes for the reasons I stated. Good luck with your application process.

As @matchakombucha mentioned, it can depend on the school and if they are accepting SAT subject test scores or not. In a typical non-pandemic year the SAT subject tests are much more important to an admissions officer. SAT subject tests can help make you stand out among other applicants (assuming you score well) and can also help demonstrate your interests to colleges. If you've taken summer classes or studied a subject on your own a subject test can prove to schools the skills and understanding you learned from that class/experience. Certain types of students might also benefit from taking subject tests (such as an ESL student) because it further demonstrates your mastery of important concepts.

Your scores on AP exams aren't really a factor at all in admissions. They can be used as a determining factor if you are on the cusp of being accepted/denied and can help prove you are competent in a subject but beyond that they don't really carry the same weight as a SAT subject test. Where AP exams are important, as was mentioned, is if you are looking to get credit for classes. However, since you're looking at highly selective schools you most likely aren't going to receive credit even with 5s. @mactchakombucha is right when they say that taking AP classes are more important than the exams themselves. AP classes show admissions officers that you are pushing yourself academically and they help increase your course rigor which is important in admissions.

If you have the time and bandwidth, both tests are worth taking. If you have to prioritize one you should be focusing your attention on the subject tests, especially for highly selective schools. Hope that helps!