And if you want differences between the two, I would say the option of using 4 extra credits on Elance to get your application on top is very stupid and Odesk has a very simple UX.
Depressing stuff like this is why I've never used the odesk acct I made a few months ago. I pretty much only visit the site when I receive email invitations to "apply" for a job, which is 90% recruiter spam and 10% unbelievably underpaid. Most recent example: "creating the official Diffbot Javascript client library"; fixed project price: $75. wat
Sometimes it makes sense to try to educate the client about this, for example pointing out that getting an oficial library for $75 can't possibly turn out well for them. Instead of wasting a little money and a lot of time and their users' goodwill, they can find someone that actually cares about the quality and charges accordingly.
Sometimes it works, sometimes not. But hey, that's sales.
As far as getting the first job is concerned, I got mine by quoting a price of $7/hour(lower than the minimum wage) and suggesting the client that he should choose python over bash for the script he wanted despite his unknown attachment with bash. And my suggestion worked out pretty well. I made an account on Odesk on 10th Dec, 2013 and I have already completed 2 projects and 3 are on progress on Odesk.