As a MSTP student, I see both graduate and medical students complain about each other (often I just keep my mouth shut about being a MD/PhD student because both groups certainly have even more negative opinions about the quality of MSTP students).
Graduate students tend to dislike the "gunner personalities" in medical school (which some medical students dislike as well). I think this is somewhat related to the importance of grades in medical school when compared to graduate school. Medical school tends to emphasize grades as a quantitative measure of success whereas graduate school emphasize the research aspect (i.e. number and quality of publications). I have seen graduate students roll their eyes everytime a medical student asks "Is this going to be on the test?" or "How can they test us on something that is not in the syllabus?"; this is especially evident when graduate students T.A. medical students.
Medical students sometimes feel that the reason graduate students are there is because they could not get into medical school. From their point of view, they don't always understand why anyone would go to graduate school given the opportunity to enroll in medical school. At some schools there is a disparity between the GPA's of the medical students and the graduate students and this further separates preconceived notions between the two schools. They also resent having to take a full course load (the equivalent of 15-18 credit hours; 3-5 classes) whereas the graduate students take 1-3 classes yet they still take the same tests and contribute to the curve. What the medical students don't often appreciate is that Ph.D. students are in lab working at the same time so even though they are taking fewer classes, the time is spent in a lab.
However, when both medical and graduate students graduate and enter academic research; I think these notions go out the window and they learn to appreciate the basic science expertise of Ph.D.s and the clinical experience of M.D.s.