The world around the camera is moving during the time camera is exposing single frame of the video and that movement makes video blurry. General rule of thumb in still photography is that you need minimum of 1/200th second shutter speed to stop nature-based movement (animals, people, etc.) and make image non-blurry. The faster you can cycle the shutter the better.
Basically, what video camera does is it takes 30 or 60 of these still photographs in a second and stitches them together using lossy compression algorithm to produce one continuous video. So, if all the other parameters stay the same then it doesn't matter if the frame rate is 1 fps or 100 fps, the only thing that counts is shutter speed used in each of the frames.
If car drives at 90 kph (approx. 56 mph) then it is moving at 25 m/s. Divide that by, let’s say 200 (for 1/200th second shutter speed) and you can see that during the exposure of one frame the camera has moved 12,5 cm (or 5 inches). When the target is moving as well, the figures can be doubled. Try moving conventional still camera 5 inches during exposure and see if the result is still sharp? If you were to use 1/30th shutter speed at 90 kph, the camera would move almost one meter during the exposure. As you can see, the exposure time needs to be much shorter than what video frame rate allows for.
But fast shutter speed (short exposure time) can't be achieved if there is not enough light, which is often case when driving. Only the brightest sunny days provide enough light for fast shutter speeds. On low light conditions camera must lower the shutter speed to brighten the image which unavoidably leads to blurry details.
Then there is other variables like pixel count (how many MP in the camera), size of individual photon detectors in the sensor, size of the sensor (surface area), lens F-number, lens coatings, bitrate target given to the algorithm, the algorithm itself, processor speed, etc., etc.
All and all, both 30 and 60 fps cameras can produce sharp details if manufacturer parametrizes them correctly, but 30 fps camera can afford to use less aggressive compression which can preserve more details without exceeding write speed of the memory card.