This is sort of like comparing oranges and apples; they are different fruit. You need to define what you mean by "competitive" and what kind of statistics will demonstrate that for you. I'm sure your answer may very according to which criteria you choose.
On the other hand, I am wondering about the motivation for your question. It's really a moot point to me, since it is likely that people who apply to one aren't going to apply to the other. My imagination is that by the time you are applying to a professional school that is as long, arduous, and expensive as either medical or dental school, you will have some clue as to which one you love. It's too difficult of a path to choose it arbitrarily in my humble opinion.
In terms of average overall GPA of a matriculant the differences between the two professions isn't profound, 3.52 for DMD/DDS (Ref:
Wikipedia; Students Admitted in 2006) and 3.64 for MD (Ref:
AAMC; Matriculants, 2006 Application Year). But this is just one number in a sea of many application elements. We all know that the application process consists of many factors, some of which are subjective. Additionally, I'm fairly sure that there are significant differences in application processes across the two professions. I wouldn't even try to compare them, as there are likely to be different elements that create a successful applicant in each profession.
Basically, I hope that whomever chooses medicine can be competitive for medical school and whomever chooses dentistry will be competitive for dental school. I happen to like "Fuji apples," so I learned how to cultivate an apple tree. It's a seedling right now, as I will be starting medical school this fall. I wish you luck in cultivating your application and much success in getting admitted into dental school.