There are a few reasons why someone might prefer to use a video site that is not the default site that Google bought.
YouTube aggressively removes content that breaks the TOS with regard to copyright or adult content. Some alternatives do not have the resources to police their own sites and some sites have less restrictive terms to start with.
YouTube shares revenue with a select few users while some other users get nothing. Sites like Revver have a policy of sharing advertising revenue with all members. That sounds great, but my experience has been that I only have five cents worth of pending payment.
Because YouTube is the default website, it bears the brunt of political censorship. A handful of countries have longstanding policies of blocking YouTube and others have done so temporarily in response to specific content. Other video sharing sites slip under the radar. I was in a second class train car in a developing country just last week and I had to walk through the first class coach in search of the snack trolley. The young dudes with the laptops were mostly watching stuff on Metacafe.