For music (ie, audio only), SoundCloud is very popular. 120 minutes free, more storage and features as you pay more. It's a bad fit for podcasters, though.
For video, I don't really see anything wrong with Vimeo aside from its lack of critical mass. YouTube still has 99% of the content you want.
If you want to share film of yourself lighting farts, you put it on youtube.
Whereas if you want to make an detailed animation about philosophy's relationship to the colour blue, then you put it on vimeo, and if it is any good then someone else will put a badly transcoded version of it on youtube, which is where most people will watch it.
For video, I don't really see anything wrong with Vimeo aside from its lack of critical mass. YouTube still has 99% of the content you want.