I happen to disagree with most of the feedback here. I have been profiting very well on Elance in only a short period of time.
It only becomes a race to the bottom if you join the race.
Ask yourself, what is your value? If you believe you can offer a service that is worth more than others, then why bid the same way as them? If you're worth more, bid more. Clients want something real, they are there to fill a gap, or have something created that they cannot do on their own, otherwise they would. They don't want someone to take a few dollars from them and then provide nothing of value.
Bidding higher works because it's real. I value my time and I value my service. The clients I have gained since being on Elance were not looking for the bottom price. They were looking for the best final value in the service they needed. There's a big difference. No, you won't win every bid. (quite frankly, you wouldn't want to). What will happen though is that by valuing yourself higher than others, and offering a better service, people recognize it within your proposal.
It's not that difficult to offer something better in your niche, most freelancers are there for a quick buck and clients know it. Provide a real service, and you will get real clients who will pay for it-- that's why they are there.
As for UpWork, I have yet to get onto it, although from what I've seen it seems like a step down from Elance. Good Luck, and if you ever need any more advice, feel free to reach out.