I think the paths are similar, but there is a key difference for me: YouTube's success didn't initially 100% rely on using other peoples copyrighted works without permission or compensation. No doubt music videos etc. helped immensely but funny cat videos and other amateur goofy content was a big part of its success. Whereas with Grooveshark, I am fairly confident that amateur authorized content doesn't factor into the equation.

That said, if the major music rights holders would just license to them from the start at affordable rates they wouldn't need to violate copyright so I suppose it's a bit of a chicken and egg problem.