The difference is a bit difficult to explain. Both have videos, forums, and wikis. Udacity courses are set up as short videos punctuated with many questions and mini assignments (running in an in-browser Python IDE), along with larger homework projects. Also, the forums are continually monitored and new videos are added to clarify concepts that students are struggling with.
In contrast, the Coursera course I'm taking (AI) has longer videos (6-20 minutes) of the instructor mumbling as he draws over and over on ever increasingly confusing Powerpoint slides. Sometimes a video will have one multiple choice question, other times the video will not have any questions at all. The worst part is that only once has the video gone on to explain the question. So if a student has a problem understanding the question, they will have to resort to the forums. There's no follow-up, unlike the questions on Udacity. At the end of each section (about an hours worth of videos) students can take a five question quiz. Granted, the feedback on the quizzes are a lot better -- but it's a lot to expect an hour of instruction to be reinforced by a mere five questions.
Basically, the Coursera course is taught as if I was sitting in a class watching an instructor draw on a Powerpoint -- the fact that it's running in a web browser and can provide a different method of teaching seems to be lost on the instructor.
Granted, this might be a critique of the instructor more than of Coursera itself -- I'm only taking a single course from them, whereas I'm taking two on Udacity. But Udacity seems to understand that you can't just take the experience of sitting in a classroom and put it online: you have to understand that this is a new medium that allows new methods of teaching.
To conclude this rambling post (sorry, I didn't know how to explain what I'm feeling as a student more concisely), if these online course ventures that are popping up all over the place are going to succeed, they are going to have to use the medium of the browser to its fullest: and in so doing, I think they will have to compete with traditional universities. That's what worries me when edX says the online classes will supplement the in-college experience: I think that you're going to have to beat the college experience to succeed in this market.