Would like to add to this thread by first saying that I do use Upwork (aka Odesk) and have been there off and on for 5 years. There are things one should know if you want to succeed there, such as knowing the platform and understanding the community.
Having said this, Upwork does not have the kind of support that VAF does.
To succeed as a VA, knowing how to start working as a VA is the tricky part. Upwork doesn't really have a system for that. They say they do, but it's not true.
Upwork is great if you want hands-on training, billing management, and a huge client base. I would recommend the site only if you prepare first.
Understand how to be a good VA first by using the great resources VAF has. When I joined Upwork, I had no clue, even with all of my corporate experience. If I had been part of VAF, I would have been in business for myself way, way sooner.
It's true that there is competition on Upwork. These days however, it's less about the 3rd world users. If you know what your doing, it will show when you reach out to prospective clients. There are a lot of US clients on Upwork who will pay very good money for US, native English speakers.
Which is how I got started 5 years ago, because back then, there were more 3rd world users, and just as many clients as now looking for users in the US. I got jobs easily once I understand the system because I marketed myself as a US, native English speaker.
Of course, this depends on what services you offer as a VA. Some niches are better then others on all the different freelancing sites. Upwork is good for long term work and VA jobs that involve long term gigs. Be aware Elance is owned by Upwork and is going bye-bye in less then 2 years.