Is it better to teach or to grade? As a graduate student at my university, I have the option many times of deciding what type of work I do for support. The two basic options are to teach either a calculus or college algebra course, or to act as TA (i.e. just hold office hours for the class, but do not teach it) and grader for an upper division (300-400 level) or early graduate course (500 level). 
Is there a hard and fast rule as to which route is a better one to take? That is, if I spend all my time TAing for say a 400 level algebra class in Galois theory, will this reflect worse on me than if I had taught several sections of introductory calculus? I am looking at this especially from the perspective of being a MS student and trying to get into a doctoral program. 
I prefer to be involved in more advanced classes as opposed to teaching a lower division course, but I do not want to cripple my chances for getting admitted into a PhD program in the near future. 
 A: I think it is probably good to try a variety of assignments over various quarters/semesters.
Personally, I find grading to be the most tedious part of teaching, and tend to avoid it when I can. On the other hand, grading can be an "easier" assignment in terms of the hours per week, and the flexibility of the hours when you work. And, as you note, grading for a more advanced class can give you an opportunity to refresh your understanding of the subject (though you should only really do this for intrinsically-motivated reasons; I wouldn't expect anyone reviewing your application to value it that much).
Teaching requires more time probably, but I never minded the preparation/lecturing all that much; the time seems to go pretty fast compared to grading (have I mentioned I don't much care for grading?). There are a host of different issues you will have to face, like controlling a classroom, public speaking, etc. but these are all valuable skills anyway (e.g. in some sense, teaching courses will prepare you for giving research talks, etc.). 
Teaching probably looks better on the application as well.
A: I agree with BaronVT, except that sometimes grading takes as much time as teaching. 
As a grad student I also preferred teaching. In order to combat the boredom of an undergraduate level class I often inserted slightly off-topic things that were not the part of the course, but enhanced good students' ability to see a bit beyond the horizon.
For example, when teaching trigonometric substitutions in freshman calculus I spend an hour explaining stereographic projection as the reason why one can expect to arrive to a rational integrand after such substitution.
Another example, when teaching assembly language programming I managed to squeeze digital logic and processor design in only 2 hours.
When the side topic is not a part of the course requirement one can glance over details and expose rather interesting things to the good students. The other ones would probably ignore your speech, but IMHO the purpose of the educator is providing the students the opportunity to advance, not making sure that each and every student would make the best of the opportunity provided.
