In a discussion with a friend of mine who is applying to graduate school in physics, she was worried that she wouldn't be able to get a good recommendation from one of her advisors because she hadn't done much creditable research under that advisor. I suggested that since she has two other recommendations from other professors who she had done research under, she could ask for a recommendation from a professor who thought highly of her academic (i.e. non-research) performance.
I was surprised by how negatively she responded to the idea: she would much prefer a mediocre letter from a research advisor than a good letter from someone who does not know her as a researcher, but does as a student. I reasoned that her research credentials would probably be spoken for with her other letters, but she didn't seem to accept this reasoning.
Is it generally true that a PhD program in the sciences looks more favorably on less-than-glowing recommendation letters about an applicant's research experience than on positive letters about his/her academic performance? Even when his/her research is attested to by other letters?
If it is not true in general, does it hold for programs in the experimental sciences? Does it vary between fields? (I am a mathematics student, and to my knowledge this question doesn't apply as well to mathematics programs.)