For "research" doctoral programs, either EdD or PhD, your "research experience or skills," along with impressive GRE & GPA, should be more helpful for you doctoral admission than teaching experiences, because, once you are in the program, you would have to go through extensive research training and produce original research results for your dissertation.
If you are interested in a "practitioner's" doctorate such as Ed.LD, your "teaching or administrative experiences" would be more important for your application.