I think the story was published in Analog. Told mostly from POV of a car. A bunch of unemployed Artificial Intelligence researchers end up at a car company and sneak a bunch of AI into the control system. Two cars start communicating with each other. The only thing they have to say is their log files of everything that ever happened to them. Once they exchange 'life stories', there's nothing left to say. Both cars figure out that the 'driver' of the car is an external component and each car has several. One car likes his drivers and optimizes performance for each of them. The other doesn't like his and quits working in the middle of an intersection with the horn blaring and the lights flashing.
This isn't quite an answer, but it won't let me comment and I think this is at least additional information: this story sounds like the short story I'm looking for that I read in a science fiction magazine like Analog (though I searched through their archives a few years ago and couldn't find it there) in mid 90's I think. The story was from the point of view of a car that did self diagnosis and fixed the problems it could. At some point, it notices an erratic signal in one of its tail lights. After analyzing the signal, it realized it was another car, a concept it hadn't considered before. After managing to communicate with the other car, it realized that it had a defective component: its driver, and the started acting up so that the driver sold it to someone else.
It's possible these are different stories, but they sound similar enough that I think we're both slightly misremembering the same story.