Regarding how well Autotrader, Cars.com or CL does; each market and situation is different (as someone pointed out). By situation, I mean that I have found (in multiple markets) that under $10k pre-owned vehicles do really well on Craigslist. That said; I am not sure that a new $80k+ luxury vehicle would do as well on CL, especially in an affluent demographic. There are always exceptions, but the rule (in my humble opinion) is that there is NO RULE, only guides. So asking if Autotrader, CL or Cars.com works and if you should keep/cancel it is a loaded question.
Back to guesstimation, as Jeff pointed out, IF you merchandise, price and promote all 3rd parties equally, you may be able to compare some things apples to apples. Even then, as someone else pointed out, many of the buyers who are educated, or who are getting educated know what they want and if it is within a reasonable distance of their home or work, will simply drive there. Even if you have a great CRM, it is ALWAYS garbage in and garbage out. Depending on the sales teams to track it accurately is risky at best, so where does that leave you? BTW, on a side note; you may want to consider moving the whole "where did you see us" questioning to finance or fulfillment coordinator (if personnel allows).
EVEN then as another pointed out, trying to quantify which resource (because many customers go to more than one site) is responsible for the "last click" is another can of worms. And even if you could quantify that; can you assure me that the last click is really responsible for the lead?
Stop the madness! This is always a lose-lose scenario and is difficult to understand ourselves let alone explain it to your employer.
Keep it simple. According to Google (ZMOT), dealers spend over 80% of the advertising budget on stimulus type of advertising. Meaning, people who really aren't in the market, majority of which aren't ready to buy, but we have to have a commercial in front of them so they have to DVR their favorite shows NOT to see your dealer slapping the hood.
Brand recognition and branding is important, but not at the expense of not being where the fish are.
People go to 3rd party sites and your site because they are IN the market to buy or are doing research to buy. Whether we like it or not, they have better brand recognition as a non-biased resource for non-loyal and even some loyal customers. I tell all dealers that for one remote, one ad in the paper or a few spots in Judge Judy that they would be better served in investing in all of them (Autorader, Cars.com, CL etc.), to ENSURE that when they are ready to buy, regardless of which major platform they use, YOU are there.
So to summarize my rant and highly opinionated post; we need to change the question. But the VDPs and SRPs and CTRs show this.... What doesn't it show? You can't manage what you can't measure, but you can reach the right audience at the right time.