I don't think Edison is available for general purchase now. You might want to click that "Sign Up" button on the page you reference to make sure you get updates.
Both Edison and Galileo are built around the Quark processor. So they will have the same core architecture but will lend themselves to different applications. Obviously the Edison is smaller and has built in wireless (Wi-Fi and BT). On the other hand, the Galileo is pin compatible with Arduino shields. I think of it like the wide array of Arduino products you see today. Similar, but with different features for different applications.
I have already signed up, and the Edison product looks like it might be exactly what I'd like for my mesh product that I'm working on.
I don't need nor want Arduino compatibility with anything really. But I do like having an embedded linux workhorse with Wifi and IO. It fits perfectly with the products I'm working on.