Craigslist is good for some things but it has a lot of trash posts. Sometimes I get lucky and someone happens to have what I want but it's easy to get bogged down by all the junk. These days if I don't find what I'm interested in there very quickly I go to someplace with a better signal/noise ratio. I wouldn't compete directly with them unless I had a way to improve that.
I mean, you spelled it out right there: if you don't find what you want on craigslist _first_, then you go someplace else. craigslist apparently has enough value, and it's easy enough to determine if you're going to get any value out of any one visit, that you don't bother going someplace else _first_. It is not a last resort visit, the craiglist competitor sites are the last resorts.
So it's the same answer again: craigslist is where majority of the users are.
http://www.angieslist.com/Angieslist/
would make for a better experience for buyers of services. But maybe that isn't the main business model of Craigslist anyway, so maybe Craigslist is happy enough with the status quo.
It's not just enough to say "we have a better search engine than google" if you want to dethrone google, you actually have to be better (although the former may get you funding). Witness Cuil. Or Live -- who tried to pay people to use their search engine: even the lure of easy money isn't enough to get people to switch. With places like craigslist and ebay, the first mover advantage is significant. These sites bring two parties together. Those who have something to sell and those who have something to buy. The sellers want to be where the buyers are and the buyers will go where the sellers are.
It is possible to have a successful business as a small time competitor to an established, entrenched player, but if your goal is to be competitive, you've got a long uphill battle ahead of you. It may be wiser to redefine the industry or look at it from another angle, then tackle that. What does craigslist do really bad that could be better? Is the lack of a competitor that eases that pain the reason why people still use the incumbent?
I'm not sure what craigslist's weak points are. The site is extremely minimal, search works reasonably well, people automatically sort most things into the right places (because otherwise they'd be wasting their time), the majority of posters don't need to pay, fraud is managed well enough that people are not looking for something else. I can't think of any weak points -- which may be why I'm not working on craigslist competitor.