Hi Kate,
I am beginning a PhD program in the Fall, so I can't offer you an inside perspective. I can, however, tell you about my experience as an applicant. Research experience does seem to matter in your application. I have been a teacher-researcher for the last four years and I believe that this was an important factor when my application was evaluated. A thesis is one type of research experience, but I think, at either place, there should be opportunities to work on research projects. It may be a good idea to contact professors at both schools with whom you would like to work if accepted. I would ask them about opportunities to work as a research assistant. I am assuming your end goal with the PhD is to teach and do research in education, therefore this is a good way to get a sense of whether the PhD is a good fit for you. If you are more practice oriented, then consider the EdD.
As far as name recognition, I personally think that matters very little on a doctoral level. I think what really matters is who you work under and how well this person is respected in your field. In my area of education, schools such as the University of Oregon and the University of Washington have greats who would be excellent doctoral mentors. In the end, well-funded institutions are also important to consider because those are the sites where cutting-edge research will be underway. I would start by looking through the literature in your field and identifying the names of people who are doing the type of work you would like to do. Then see what universities these people teach at and apply to those first. These may be "big name" schools, or they may not be.
Good Luck! I hope you find a school that is a perfect match!