Though Coursera's Stanford course and SEE's course are taught by the same professor, they are different. The Coursera one is 229A(pplied) and doesn't really explore the math behind the techniques; the SEE one is the original 229 that most Stanford students take, and is significantly more math-intensive. The 229A page explains the differences well [1]:
> Q: How does CS229A relate to CS229? Which should I take?
> A: CS229A is complementary to CS229, and provides more applied skills. It's okay to take both, though enrollment in CS229A is limited, and we may give priority to students who have not taken and who are not taking CS229. If your goal is a deep mathematical understanding of machine learning, or if your goal is to do research in AI or machine learning, you should definitely take CS229 (either instead of, or in addition to, CS229A). CS229 has a more difficult set of prerequisites. If you are interested in machine learning but aren't sure if you're ready for the mathematical depth that CS229 requires, then consider taking CS229A instead.
I haven't taken Washington's course, but it seems to be more comprehensive than both of Stanford's. It's currently only available in preview mode, though, so you won't have access to quizzes and programming assignments, which are vital for comprehension and retention.
If you're interested in getting started with machine learning and want to solving problems with it, I'd suggest the Coursera Stanford one. If you're interested in theory, go with the SEE one. I'm not familiar with the Washington one, but I don't recommend it as your primary course as it's still in preview mode, and only the lectures are available.
1. http://cs229a.stanford.edu/faq.html