Teaching assistantships for higher-level undergraduate courses will require experience both in the theory and practice of the discipline. For example, a student with just a few graduate courses completed isn't likely to be chosen over a Ph.D. candidate who has already completed a master's degree and who has already taught lower-level undergraduate courses. Furthermore, the professor overseeing the course may have specific expectations that require advanced knowledge in a particular area of the discipline.
In order to be eligible for a teaching assistantship, most universities require that the applicant be in good academic standing. Good academic standing at the graduate level means a grade point average (GPA) of no less than 3.0. Indeed, many universities will expect or demand a 4.0 GPA. The department chair will make sure that there are no incompletes on the applicant's record and that the applicant is on track for completing his degree on time. In other words, if the applicant has completed comprehensive exams and is past due for completing his dissertation, the university is less likely to select him for a teaching assistantship.
Higher-level undergraduate courses move away from generalized study and towards specialized study. Teaching assistantships for these courses follow the same trend. Thus, an applicant who intends to specialize in the field that is being taught is more likely to be chosen for the position than an applicant who will specialize in a different field within the discipline. Experience teaching an upper-level undergraduate course will lay the proper foundation for teaching graduate-level courses after the graduate student has earned his Ph.D. and has taken a full time position at another university. For those who don't intend to work within academia, research assistantships may be more appropriate.