I have tested both the 100-400 side by side with the 70-200 with an extender, I can provide you with the images if you want.
The 100-400 is a clear winner to me. Sharper than the 70-200 with an extender, but the biggest thing is the weight. The 100-400 is only half the weight of the 70-200.
I use it to shoot aircraft, and after holding the lens and camera at head height for the whole day, I appreciate the lighter weight of the 100-400 so much. Plus the 70-200 with extender is not as sharp, at least the one I used. I even tested the extender with the 100-400 to check the extender was not the cause of the loss of quality.
The only benefit to the 70-200 is that you have a good lens that you can use inside when you are not shooting cars. The 100-400 is useless inside. But I didn't buy it for that, I bought it for my photography business outside.
The test gallery on my outdated site is here:
http://www.aussietimmeh.com/gallery/v/tech/400test/
Be sure to expand each image out to full size to get a better idea of the differences.
Hope it helps.