Their marketing and brand are the most important aspects. Bing proxies are a-dime-a-dozen but only DuckDuckGo has achieved tremendous media attention and funding.
One of the proxies had to win out, right? We're only talking about DuckDuckGo and not BearBearClaw because they survived. I don't think they're doing anything particularly special. They're also a much older company with a lot smaller search volume than people realize.