I have both. I can't seem to pass the oDesk Readiness Test to increase my applications. I even had my husband help me. I did the ID verification for oDesk. I really like oDesk over all. I've had offers, but as of late they haven't lined up well with my schedule.
I like eLance as well. They do their ID verification for Skype. I missed my appointment and I haven't had time to reschedule it. :-/ I haven't received any offers from eLance, but honestly I haven't used it much.