For example, are the curriculum and exam for AP Chem comparable to general chemistry? Or does it depend on the school?
It depends on both the high school and the college. There has been lots of discussion on CC about the variability in high school courses.
In terms of whether the content tested in the AP exams is considered by colleges to indicate knowledge equivalent to that learned by taking the college course, that can vary by college (although it varies more for some AP exams than others). You can check the AP credit listings on various college web sites to see what subject credit and advanced placement each college gives.
For AP chemistry specifically, subject credit can vary from none to two semesters / three quarters of college general chemistry, and may vary by major (e.g. may be considered equivalent to general chemistry for non-chemistry majors but not for general chemistry for chemistry majors). Pre-meds also need to consider medical school expectations of college courses versus AP credit for pre-med courses.
Both of my sons took AP Calculus AB and scored 5 on the exams.
My oldest attended Case Western and started in Calc 2. His professor gave a quiz on the second day of class. He told the class he gave it so that the students who are starting in Calc 2 would know if they should start in Calc 1. He told them if they got less than 85% on the quiz they should drop to Calc 1. My son got 100% on the quiz and wound up with an A in the class. My son told me that much of Calc 2 had been covered in his high school class. This son was a math major.
My youngest attended Haverford and took a placement exam. He placed into the third semester of calculus. He went to the professor because he was concerned that there were a few topics that were not covered in his high school class that were part of Calc 3. The professor told him that he was aware of the handful of topics not normally covered and that he would reteach those topics (as this occurs all the time). He wound up with a 3.7 in the class. He is a history major.
It seems like students who did well in Calculus AB get most of the college curriculum the course is supposed to cover.
It really depends upon the college. As a general statement, Calc AB, Calc BC, Microeconomics, Macroeconomics, Physics C: Mech, and Physics C: E&M most closely align content-wise with college courses.
For some colleges, their intro calc/econ/physics classes may cover more depth than AP (e.g. clac may be more proof-based). And of course, credit policies vary with the school
I’ve heard from a math professor at a prominent NYC university say that not everything that s/he wishes the AP students would take Calc 1 there, because they cover topics not covered in the AP course.