My favorite thing about getting Cajun from CL is that there were 0 hoops to jump through. Not because her owner didn't care where she went (and I think she legitimately DID care, as she had apparently turned away a couple people), but there wasn't that annoying rescue process with the lengthy application, the reference checks, the home visit. My only rescue experience is with Happy, and I think they sped through the process quite a bit with her, but it irked me that I had to go into details about my other pets and prove this, that, and the other thing about them and have them current on vaccines and defend why my cat wasn't current blah blah blah.
There was this nagging feeling with Cajun that maybe there was a story we weren't getting, she SAYS she just doesn't have time for her but maybe she's really just crazy and aggressive and is going to eat the other dogs? But really all we had to do was spend some time with her to feel pretty confident with our decision.
I don't tend to see "my" type of dogs advertised on CL, but as a general rule I'd probably be more likely to get a dog off CL than I would be to go through a rescue.