I've used the 1.4x III with both the 70-200 and the 100-400L II. I encourage you to inspect recent images in the UHH photo gallery from both the Chicago (all of the Blue Angels images) and the Cleveland airshows (final two Thunderbirds) in 2017. You can assess with your own eyes the relative quality of the results with an extended 100-400L II. The AF is slightly less responsive on the 100-400 when extended and use of AI Servo and BBF is a tip encouraged when using the 1.4x.

From a practical standpoint, if you want to shoot at 400mm, the 100-400L II is a better choice. The results will be sharper between 100 and 400 than the 70-200 extended by the 2x as well as having a wider aperture available during shorter portions of the zoom.

The 70-200 extended to just 280mm doesn't buy you that much if you own the 100-400L II. Use of the 1.4x on the 70-200 is not discernable in the results if stepped down to f/5 or smaller. I was using the lens within the zoom range anyways and found the 1.4x accomplished nothing other than limiting the max aperture. The 70-200 is more beneficial for the f/2.8, the amazing IS and the AF speed than it's ability to be extended to 280mm or 400mm.

Given the negligible difference between 70mm and 100mm, the 100-400L II is more versatile than the 70-200 f/2.8L IS in all situations except indoors / lowlight. The lenses are roughly the same size and weight.