As someone who has been teaching for some time now, hopefully I'll be able to provide you with insight.
The major difference is that PhD programs are often full-time programs (at least for a couple of the semesters during which you're an enrolled student). EdD programs, however, are usually part-time programs that are not as research-driven, but rather coursework driven. EdD programs generally culminate in a capstone Thesis, but it's quite different from the process that leads to a PhD thesis.
EdD programs are typically designed for individuals who are practicing teachers or administrators, while PhD programs are designed for students who can commit to full-time study.
As for which is better- It depends entirely on your ultimate career goals. If you would like to be a practicing educator, then I would highly recommend finding a job where you can use your degree, and then enroll in a part-time EdD program. If you want to teach at a research-oriented university, then definitely pursue your PhD.
I hope this clears up your questions.