How does the choice of grading scale (such as A = 90+, B=80-90, etc.) affect an undergraduate program? I am a math professor at a mid-tier state university in the US. Most classes here, including math classes, use either a ten-point scale (A = 90+, B=80-89, C=70-79, D=60-69, F=0-59) or something close to it.

Here this is widely considered to be "common sense", so much so that I raised eyebrows when I questioned it. However, I'd never seen it in common use at any of the universities (also in the US) where I'd studied or taught. I was more familiar with a system where assessments would be harder, and the cutoff for an A would usually be between 60 and 85.

The choice of grading system has a lot of potential effects on student and instructor expectations, on what sort of goals may be realistically set, and what students consider themselves accountable for.

Are there any studies as to the advantages and disadvantages of each system?
Using the grading cutoffs that students are familiar with leads to fewer complaints by the students, so I'd highly recommend sticking with it.  There's a lot of anxiety around grades, and the clearer the rules are and the less unusual they are the more comfortable the students feel. The grade scale doesn't actually matter, because you just curve up the exams so that the grades you think the work deserves gets adjusted to the fixed scale.  You can still write exams where a 65% is an A, you just apply a curve so that 65 gets entered as a 90.