It will vary somewhat with the actual conditions, but in general, if you open the aperture diaphragm, a shorter exposure time will be needed, so Case 1 will show more movement of car headlights. Stopping down (closing the aperture diaphragm) will require a longer shutter speed for the same exposure, so you'll get longer trails.
Whether this happens under condition 2 or not depends on how long the exposure time ends up being for the particular scene, and that depends on a number of factors. Lenses vary, so the difference from your two cases could be two stops (4× faster shutter) or it could be nine stops (500× faster!).
The result will also depend on the amount of ambient light and how fast the cars are traveling. A longer exposure (with a closed-down aperture) will be more apt to reduce the cars themselves to a blur, possibly leaving only the lights visible.
The nice thing about digital is that you can experiment. You can shoot in manual mode, or use shutter priority (often labeled
Tv for "time value") mode, which will let you control the time while setting the aperture automatically (in that case, you may want to use negative EV compensation). Start with an exposure of, say, 1 second and whatever aperture combination works to get the exposure you want. Review the result, and increase the time if you want more streaking. If long exposure is your intent, you probably want to fix the camera to a low ISO, but if it's dark and you want to include some of the ambient scene without having to put the shutter to several minutes, you might try raising that as well.