I just picked up the 70-300 and have only used it a couple of times with the 1.4 ext. I already find it quite handy as it gets you out further than the 100-400 (compared to without the ext. of course) at such a smaller/lighter size/weight. I also have the 100-400, and my first impression is that it might even be a bit more responsive on the 70-300 than the 100-400. Maybe because it's moving less glass/weight on the 70-300, or maybe just my imagination. I plan to test some more, but it will likely replace my 100-400 for most telephoto needs.
With regard to the park itself, I'd agree with what others have said. You can end up all over the focal length range. If you have the ability, you might consider two bodies. Maybe rent if that's a consideration. Something wide/normal on one, and then the 70-300 on the other. Last time I went to Yellowstone, it was early October, and it was still a bit on the busy side with traffic. One evening, it took over an hour to move about 5-10 miles to get out of the West Yellowstone gate. The northern and eastern parts of the park did seem less busy. I can only imagine how crazy summer could be with school out! Almost everywhere you look, you'll want to point your camera and take a picture.
-Matt