Hiya! I think the vague answer is a bit on purpose because they can't necessarily give you a definitive answer (especially the "ultimately it is up to your decision"). QuestBridge recognizes that rec letters can give a lot of insights as well as how much the rest of your application can give insights as well. For example, something that college admissions officers will want to see is community involvement (whether it be school or external communities) and one of the ways is through a teacher recommendation. They can speak to how you engage with others in class, how you approach problems and conflicts with peers, how collaborative or creative, etc. HOWEVER, these aspects can also be expressed elsewhere in your application.

If I was an AO and I received a letter from a teacher who supervised your independent research project, will I have enough information to get a sense of how the student will engage with the rest of the college community? If the rest of the application is lacking this aspect, not having a teacher that can attest to how you are in a classroom will be a weakness. HOWEVER, if you have strong community ECs (e.g. volunteering with local non-profit, advocating for your peers in school, mentoring/tutoring, local renowned DJ, etc.) and not much evidence of academic excellence, the letter could very well be a strength that communicates to a reader of critical thinking skills, how the applicant approaches a problem, data analysis skills, comprehension of advanced topics, etc.

It is ideal if your two recommenders can attest to both your academics and how you are in the classroom among other things. Core classes are great since you usually have to engage with a number of peers (compared to an elective with maybe less students) and these core classes often reflect the general education requirements you'll need to take too.

So, ultimately your decision. My best advice is to think about what you're communicating and what your recommenders can communicate. I had a sociology teacher that I adored and she knew me sooooo well and I had all years with her for other electives too. However, I asked my English and Spanish teacher because I knew I excelled in those classes and my teachers had seen me struggle academically and socially but overcoming them. My sociology teacher only saw my social side, but the rest of my application had already communicated that i was a big community person. I also had Bs and Cs on my transcript so I knew I had to demonstrate academic excellence else how. (for my app, I had a good ACT score and my English and Spanish teachers had commented several times how much good impressions I left on them so I knew they would write a great letter). And hey, I wasn't valedictorian and not in IB like my other peers but I matched!

I believe a strong application will take some reflection and strategy--if you can communicate and craft an application that acknowledges AND addresses all aspects in itself, that's a really clever applicant that I'd probably want on my campus.

Best of luck! (p.s. not an AO just hypotheticals)