I like Elance.
I found Odesk kind of cumbersome to use. Odesk also seemed to have more emphasis on Skype and invasive software like keyloggers. I didn't feel comfortable with that.
In my area of expertise, the jobs on Odesk were also fewer and less lucrative than Elance. After getting a profile set up on Odesk, I could never pull the trigger on bidding on jobs, due the my concerns.
It can be hard to get started - but once you get a couple of reviews under your belt, people have more confidence with hiring you.
My biggest issue has been with people not adequately disclosing the scope of their projects. Then once you've committed, they spring a bunch of extras on you. Given the importance of maintaining a 5-star rating from your clients, you can get into a sticky situation where you don't want to jeopardize your rating by angering that client.
The vast majority of clients have been good clients, though. I have had no trouble getting paid, either. Overall, the rate of pay is less than from local clients, but the client base is much broader.