Should you request graduate school recommendation letters only from those that know you as a researcher? 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.)
Graduate schools admitting students are looking for evidence of ability as (or at least strong potential to become) a good researcher. Therefore, letters of recommendation that do not discuss research at all are simply not nearly as helpful to us than letters that do.

However, a mediocre letter of recommendation can be damaging to a student's chances of admission. Someone who isn't enthusiastic and immediately willing to write a letter should not be asked to write one; the "hit" to the student's admission chances simply aren't worth it.

So, under the circumstances, someone who is willing to write a very good letter that can testify to academic talent is certainly better than a weak to mediocre research-based letter. But a letter that only talks about a student taking tests well and "acing" a class is not really helpful. A letter that talks about, for instance, an in-depth class assignment, or can include details and observations from outside of class, would make for a much stronger and more useful letter.