Should I do IB or AP?

I’m registering for classes soon and I still can’t decide whether or not to take the AP route or the IB route. My school’s IB program is a two year program where students take all IB classes for junior and senior year. My school also offers many APs, but I’m not sure which route is best for me as my guidance counselors have not been that helpful and the AP and IB teachers are typically biased. Here is the list of courses our IB program offers, all of which I would take except for IB Physics:

IB Mathematics SL (covers a range of math topics as well as AB calc material)
IB English HL
IB Biology SL/HL
IB Physics SL
IB Chemistry SL
IB History HL
IB Language (Spanish, French, Chinese, etc.) SL
TOK/ITGS and those other IB classes

If I were to take the AP route, here are the classes I would take:

(Junior Year)
AP AB/BC Calc
AP English
AP Chem
AP US History (semester- first half taken over summer)
AP Physics 1 (semester)

(Senior Year)
AP Stat
AP Spanish
AP Bio
AP Physics 2 (semester)
English 4 Honors (semester)

I know I’m missing a history in senior year but I’m taking AP gov and AP micro right now so I’ll have enough social studies credits.

I want to pursue a career in math and science and perhaps become a chemical engineer. As you can see, our IB program is not that strong in those subjects as HL math and chemistry are not offered. Most students at my school view our IB program in a negative light due to all the work and writing and the Extended Essay that the program requires, but they do say it prepares you well for college. However, you cannot get college credit with IB SL classes. I figured if I did IB, I would just self study for the AP exams, but I know that could be difficult and I’m not guaranteed a 5. Our counselors mark our IB program as the most rigorous route on college applications. I know colleges want you to take the most rigorous courses, so should I do IB solely for that reason? Or should I do AP in order to get a stronger math and science background? I would love to go to a top engineering school, and I know they like to see classes like AP Calculus on your application, something I would not have if I went down the IB route.

In addition, if I received all A’s, my weighted GPA would be much higher with IB, and I would have a much higher class rank. I know a lot of top colleges look at class rank, so is that another reason I should do IB?

If you want to get into selective colleges, that “most rigorous” checkbox will matter far more than taking Math or Chem HL. The higher GPA also matters a lot for class ranking, so IB seems statistically the better choice.

That being said, if you have a deep interest in the fields not covered by the IB courses and can’t wait till college to go more in depth, take AP.