I own the 70-300L and have used the 100-400L also. They are more different lenses than their numbers suggest. The 100-400mm is more of a 'bird specialist' and often focal length limited answer, whereas the 70-300mm is more of a general purpose telephoto zoom.
For me, the choice to go 70-300L was mainly on its much superior portability. Furthermore for most of my telephoto shots, 300mm on my Canon 7D (equivalent to 480mm in FF / 35mm format) was sufficiently.
The 70-300L does have much better IS (4 stops vs 2 stops on the 100-400L) which does make a lot of difference. I don't like the 100-400L's pull-zoom action.
Good copies of both lenses can produce great photos when used by experienced and knowledgeable users. Though I would say that on the whole, the 70-300L has superior IQ (mine is particularly sharp and contrasty at all focal lengths, even wide open).
If I only had a FF camera - then the 70-300L wouldn't probably be enough reach for more of my needs. I have recently used a 5DmkIII and the difference from 1.6x crop to FF is remarkable, so I would be 'stuck' - because I'm not so keen on the size and handling of the 100-400L. But with my 7D, the 70-300L does the 'trick' - even making a handy candid / portrait lens.
I really appreciate how good the 70-300L is as a travel combination with my 7D and 15-85mm lens. I fit both in my shoulder LowePro bag often when I'm out taking photos. And I can shoot all day with this 2 lens combination.
Hope my perspective is helpful.