It would appear that basically Adobe Edge Web Fonts is a free version of TypeKit. TypeKit is a fantastic typeface solution for the web. I use it on many sites. The service does not cost much and has an incredibly selection.
Some may find it odd that I will start a new web project with the typeface. I want to find a typeface or pair typefaces with that business's personality. Since type can say so much, it's important I get that right, so I do it first.
I imagine the selection of free typefaces on Adobe Edge Web Fonts will be nice, but not a robust as the paid versions at TypeKit. For me, I want quality. I gladly pay for TypeKit. I feel good knowing I have am giving back to the typefaces founders for their hard work.
You can read more about TypeKit and Adobe Edge Web Fonts on their official site.