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I've no data to back up which works better from a conversion standpoint, but purely on user experience I think that the inline (Facebook style) chat is much friendlier to use. The key thing is that it persists the conversation history when the user clicks across pages and that the skin of the chatbox can be sufficiently customized to fit into the look and feel of your website. A particular gripe I have with a lot of dealer websites is that add-on widgets (not built by the website provider) such as live chat or coupon incentives have a look and feel totally at odds to the site itself.

Another potential turn-off for shoppers would be seeing a different website domain in the new popup window.

A non-automotive inline chat solution which I really like is Olark. Fits very easily into your website design.